{"id":297425,"date":"2023-12-19T11:35:21","date_gmt":"2023-12-19T04:35:21","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=297425"},"modified":"2025-12-20T14:50:18","modified_gmt":"2025-12-20T07:50:18","slug":"giai-phuong-trinh-bac-2","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/","title":{"rendered":"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (To\u00e1n l\u1edbp 9)"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (a \u2260 0) l\u00e0 x = [-b \u00b1 \u221a\u0394] \/ (2a), v\u1edbi \u0394 = b\u00b2 &#8211; 4ac l\u00e0 bi\u1ec7t th\u1ee9c. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c c\u1ed1t l\u00f5i To\u00e1n l\u1edbp 9, gi\u00fap gi\u1ea3i nhanh m\u1ecdi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0394 &gt; 0 (hai nghi\u1ec7m ph\u00e2n bi\u1ec7t), \u0394 = 0 (nghi\u1ec7m k\u00e9p), \u0394 &lt; 0 (v\u00f4 nghi\u1ec7m), k\u00e8m v\u00ed d\u1ee5 v\u00e0 b\u00e0i t\u1eadp th\u1ef1c h\u00e0nh.<\/span><\/p>\n<h2>\u0110\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h2>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 m\u1ed9t lo\u1ea1i ph\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc c\u00f3 d\u1ea1ng \u0111\u1eb7c bi\u1ec7t, trong \u0111\u00f3 c\u00f3 m\u1ed9t s\u1ed1 h\u1eb1ng s\u1ed1 v\u00e0 m\u1ed9t bi\u1ebfn s\u1ed1 c\u00f3 <strong>s\u1ed1 m\u0169 l\u00e0 2<\/strong>. D\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n c\u00e1c quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn s\u1ed1 trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau nh\u01b0 v\u1eadt l\u00fd, k\u1ef9 thu\u1eadt, kinh t\u1ebf, khoa h\u1ecdc t\u1ef1 nhi\u00ean,&#8230; Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u0169ng l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 quan tr\u1ecdng trong vi\u1ec7c nghi\u00ean c\u1ee9u c\u00e1c h\u00e0m s\u1ed1 c\u00f3 d\u1ea1ng t\u01b0\u01a1ng t\u1ef1, \u0111\u01b0\u1eddng cong c\u00f3 h\u00ecnh ch\u1eef U, \u0111\u1ecbnh l\u00fd v\u1ec1 tam gi\u00e1c vu\u00f4ng v\u00e0 nhi\u1ec1u kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc kh\u00e1c.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/giai-phuong-trinh-bac-2-2\/\" rel=\"attachment wp-att-297441\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-297441 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2.jpg\" alt=\"giai-phuong-trinh-bac-2-2\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>Hi\u1ec3u \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 kh\u00f4ng ch\u1ec9 gi\u00fap b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc c\u01a1 b\u1ea3n, m\u00e0 c\u00f2n gi\u00fap b\u1ea1n \u00e1p d\u1ee5ng v\u00e0o c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y. B\u1ea1n c\u00f3 th\u1ec3 d\u00f9ng ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 \u0111\u1ec3 t\u00ednh to\u00e1n chi ph\u00ed, l\u1ee3i nhu\u1eadn, di\u1ec7n t\u00edch, th\u1ec3 t\u00edch, kho\u1ea3ng c\u00e1ch, t\u1ed1c \u0111\u1ed9,&#8230; B\u1ea1n c\u0169ng c\u00f3 th\u1ec3 d\u00f9ng ki\u1ebfn th\u1ee9c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y \u0111\u1ec3 m\u00f4 h\u00ecnh h\u00f3a c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng t\u1ef1 nhi\u00ean nh\u01b0 s\u1ef1 bi\u1ebfn \u0111\u1ed5i nhi\u1ec7t \u0111\u1ed9, \u0111\u1ed9 cao, \u00e1p su\u1ea5t,&#8230;<\/p>\n<p>B\u1eb1ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ecm nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm ra c\u00e1c nghi\u1ec7m hay c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn s\u1ed1 th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh. T\u1eeb \u0111\u00f3 suy ra c\u00e1c k\u1ebft lu\u1eadn hay gi\u1ea3i th\u00edch cho c\u00e1c b\u00e0i to\u00e1n kh\u00e1c nhau. Tuy nhi\u00ean t\u00f9y v\u00e0o t\u1eebng tr\u01b0\u1eddng h\u1ee3p m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng nh\u1eefng ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c nhau.<\/p>\n<h2>H\u01b0\u1edbng d\u1eabn ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 \u0111\u01a1n gi\u1ea3n nh\u1ea5t<\/h2>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n trong to\u00e1n h\u1ecdc v\u00e0 vi\u1ec7c gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 th\u1ec3 g\u00e2y kh\u00f3 kh\u0103n \u0111\u1ed1i v\u1edbi nhi\u1ec1u ng\u01b0\u1eddi. Tr\u00ean th\u1ef1c t\u1ebf, c\u00f3 m\u1ed9t c\u00e1ch t\u00ecm nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 \u0111\u01a1n gi\u1ea3n nh\u1ea5t m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng. V\u1edbi h\u01b0\u1edbng d\u1eabn sau \u0111\u00e2y, ch\u00fang ta s\u1ebd kh\u00e1m ph\u00e1 quy tr\u00ecnh t\u00ecm nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng v\u00e0 hi\u1ec7u qu\u1ea3.<\/p>\n<h3>S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m \u0111\u1ec3 t\u00ednh ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h3>\n<p><b>C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 \u0111\u1ea7y \u0111\u1ee7:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">x = [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)] \/ (2a), v\u1edbi \u0394 = b\u00b2 &#8211; 4ac.<\/span><\/p>\n<p><b>C\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn (khi b ch\u1eb5n):<\/b><span style=\"font-weight: 400;\"> x = [-b&#8217; \u00b1 \u221a(b&#8217;\u00b2 &#8211; ac)] \/ a (b = 2b&#8217;).<\/span><\/p>\n<p><b>C\u00e1c tr\u01b0\u1eddng h\u1ee3p:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0394 &gt; 0: Hai nghi\u1ec7m ph\u00e2n bi\u1ec7t x\u2081 = [-b + \u221a\u0394]\/2a; x\u2082 = [-b &#8211; \u221a\u0394]\/2a.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0394 = 0: Nghi\u1ec7m k\u00e9p x = -b\/2a.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0394 &lt; 0: V\u00f4 nghi\u1ec7m th\u1ef1c.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: Gi\u1ea3i x\u00b2 &#8211; 5x + 6 = 0 \u2192 \u0394 = 25 &#8211; 24 = 1 &gt; 0 \u2192 x\u2081 = 3; x\u2082 = 2.<\/span><\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/giai-phuong-trinh-bac-2-3\/\" rel=\"attachment wp-att-297442\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-297442 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3.jpg\" alt=\"giai-phuong-trinh-bac-2-3\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>\u0110\u1ec3 nh\u1edb c\u00f4ng th\u1ee9c nghi\u1ec7m n\u00e0y v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u1ed9t s\u1ed1 c\u00e1ch nh\u1edb \u0111\u01a1n gi\u1ea3n. M\u1ed9t c\u00e1ch l\u00e0 ghi nh\u1edb c\u00e1c k\u00fd t\u1ef1 trong c\u00f4ng th\u1ee9c v\u00e0 quan s\u00e1t m\u1ed1i quan h\u1ec7 gi\u1eefa ch\u00fang.<\/p>\n<p>V\u00ed d\u1ee5, trong c\u00f4ng th\u1ee9c nghi\u1ec7m, ta c\u00f3 c\u00e1c k\u00fd t\u1ef1 a, b, c, \u00b1, \u221a, ^2, -, 4 v\u00e0 2. B\u1ea1n c\u00f3 th\u1ec3 t\u01b0\u1edfng t\u01b0\u1ee3ng r\u1eb1ng &#8220;a&#8221; \u0111\u1ee9ng tr\u00ean \u0111\u1ec9nh v\u00e0 &#8220;b&#8221; v\u00e0 &#8220;c&#8221; n\u1eb1m d\u01b0\u1edbi. D\u1ea5u &#8220;+\/-&#8221; th\u1ec3 hi\u1ec7n s\u1ef1 l\u1ef1a ch\u1ecdn gi\u1eefa d\u1ea5u c\u1ed9ng v\u00e0 d\u1ea5u tr\u1eeb khi t\u00ednh to\u00e1n. D\u1ea5u &#8220;\u221a&#8221; bi\u1ec3u th\u1ecb c\u0103n b\u1eadc hai, &#8220;b^2&#8221; l\u00e0 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a b, c\u00f2n &#8220;4ac&#8221; l\u00e0 t\u00edch c\u1ee7a 4, a v\u00e0 c. B\u1eb1ng c\u00e1ch ghi nh\u1edb v\u00e0 li\u00ean k\u1ebft c\u00e1c k\u00fd t\u1ef1 n\u00e0y, b\u1ea1n c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng nh\u1edb c\u00f4ng th\u1ee9c nghi\u1ec7m.<\/p>\n<p>M\u1ed9t c\u00e1ch kh\u00e1c \u0111\u1ec3 ghi nh\u1edb c\u00f4ng th\u1ee9c nghi\u1ec7m l\u00e0 h\u1ecdc thu\u1ed9c m\u1ed9t c\u00e2u th\u01a1 nh\u1edb. Ta c\u00f3 c\u00e2u th\u01a1 &#8220;B\u00e9 b\u1ecf \u0111i, b\u00ecnh ph\u01b0\u01a1ng tr\u1eeb b\u1ed1n a c\u1ed9ng, Hai a chia, c\u0103n b\u1eadc hai c\u1ed9ng tr\u1eeb&#8221; c\u00f3 th\u1ec3 gi\u00fap b\u1ea1n nh\u1edb c\u00e1c b\u01b0\u1edbc t\u00ednh to\u00e1n trong c\u00f4ng th\u1ee9c nghi\u1ec7m. C\u00e2u th\u01a1 n\u00e0y l\u1ea7n l\u01b0\u1ee3t \u0111\u1ec1 c\u1eadp \u0111\u1ebfn vi\u1ec7c b\u1ecf d\u1ea5u tr\u1eeb, t\u00ednh b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a b v\u00e0 tr\u1eeb \u0111i 4ac, sau \u0111\u00f3 chia cho 2a v\u00e0 cu\u1ed1i c\u00f9ng t\u00ednh c\u0103n b\u1eadc hai v\u00e0 c\u1ed9ng ho\u1eb7c tr\u1eeb.<\/p>\n<h3>T\u00ednh to\u00e1n v\u00e0 gi\u1ea3i th\u00edch qu\u00e1 tr\u00ecnh \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m<\/h3>\n<p>\u0110\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2, b\u1ea1n c\u1ea7n th\u1ef1c hi\u1ec7n c\u00e1c thao t\u00e1c sau \u0111\u00e2y:<\/p>\n<p>B\u01b0\u1edbc 1: X\u00e1c \u0111\u1ecbnh c\u00e1c h\u1eb1ng s\u1ed1 a,b,c trong ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2. B\u1ea1n c\u1ea7n ch\u00fa \u00fd r\u1eb1ng a l\u00e0 h\u1ec7 s\u1ed1 c\u1ee7a x2 , b l\u00e0 h\u1ec7 s\u1ed1 c\u1ee7a x\u00a0 v\u00e0 c l\u00e0 h\u1eb1ng s\u1ed1 t\u1ef1 do. N\u1ebfu ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng c\u00f3 m\u1ed9t trong ba h\u1eb1ng s\u1ed1 n\u00e0y, b\u1ea1n c\u00f3 th\u1ec3 coi h\u1eb1ng s\u1ed1 \u0111\u00f3 b\u1eb1ng 0.<\/p>\n<p>B\u01b0\u1edbc 2: Thay c\u00e1c h\u1eb1ng s\u1ed1 v\u00e0o c\u00f4ng th\u1ee9c nghi\u1ec7m v\u00e0 t\u00ednh to\u00e1n gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c b\u00ean trong c\u0103n b\u1eadc hai, g\u1ecdi l\u00e0 bi\u1ec7t th\u1ee9c delta (\u0394 ). Bi\u1ec7t th\u1ee9c delta l\u00e0 m\u1ed9t s\u1ed1 quan tr\u1ecdng, v\u00ec n\u00f3 quy\u1ebft \u0111\u1ecbnh s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh. Bi\u1ec7t th\u1ee9c delta c\u00f3 c\u00f4ng th\u1ee9c l\u00e0 <strong>\u0394=b2\u22124ac.<\/strong><\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/giai-phuong-trinh-bac-2-4\/\" rel=\"attachment wp-att-297443\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-297443 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4.jpg\" alt=\"giai-phuong-trinh-bac-2-4\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-4-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>B\u01b0\u1edbc 3: Ki\u1ec3m tra gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec7t th\u1ee9c Delta \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<ul>\n<li>Trong tr\u01b0\u1eddng h\u1ee3p \u0394&gt;0 th\u00ec ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t.<\/li>\n<li>N\u1ebfu \u0394=0, ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m k\u00e9p. C\u00f2n n\u1ebfu \u0394&lt;0 th\u00ec ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd v\u00f4 nghi\u1ec7m.<\/li>\n<li>N\u1ebfu bi\u1ec7t th\u1ee9c delta l\u00e0 m\u1ed9t s\u1ed1 \u00e2m, b\u1ea1n kh\u00f4ng th\u1ec3 l\u1ea5y c\u0103n b\u1eadc hai c\u1ee7a n\u00f3. V\u00ec trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng c\u00f3 nghi\u1ec7m th\u1ef1c.<\/li>\n<\/ul>\n<p>B\u01b0\u1edbc 4: T\u00ednh to\u00e1n gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c nghi\u1ec7m b\u1eb1ng c\u00e1ch thay gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec7t th\u1ee9c Delta v\u00e0o c\u00f4ng th\u1ee9c nghi\u1ec7m v\u00e0 l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 n\u1ebfu c\u1ea7n. H\u00e3y ch\u00fa \u00fd r\u1eb1ng c\u00f4ng th\u1ee9c nghi\u1ec7m c\u00f3 hai d\u1ea5u c\u1ed9ng\/tr\u1eeb (\u00b1). V\u00ec v\u1eady c\u1ea7n t\u00ednh to\u00e1n hai gi\u00e1 tr\u1ecb c\u1ee7a x v\u1edbi hai d\u1ea5u n\u00e0y. B\u1ea1n c\u0169ng c\u1ea7n ch\u00fa \u00fd r\u1eb1ng n\u1ebfu bi\u1ec7t th\u1ee9c Delta b\u1eb1ng 0, b\u1ea1n ch\u1ec9 c\u1ea7n t\u00ednh to\u00e1n m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a x, v\u00ec hai nghi\u1ec7m tr\u00f9ng nhau.<\/p>\n<h2>M\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 kh\u00e1c<\/h2>\n<p>Ngo\u00e0i c\u00e1ch t\u00ecm nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 \u0111\u01a1n gi\u1ea3n nh\u1ea5t m\u00e0 ch\u00fang ta \u0111\u00e3 kh\u00e1m ph\u00e1 \u1edf tr\u00ean, c\u00f2n t\u1ed3n t\u1ea1i m\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y. T\u00f9y thu\u1ed9c v\u00e0o d\u1ea1ng v\u00e0 \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 l\u1ef1a ch\u1ecdn ph\u01b0\u01a1ng ph\u00e1p ph\u00f9 h\u1ee3p nh\u1ea5t \u0111\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c b\u00e0i to\u00e1n.<\/p>\n<h3>Xem x\u00e9t c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h3>\n<p>Trong qu\u00e1 tr\u00ecnh t\u00ecm nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2, ch\u00fang ta c\u1ea7n xem x\u00e9t c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t \u0111\u1ec3 nh\u1eadn bi\u1ebft nghi\u1ec7m m\u1ed9t c\u00e1ch nhanh ch\u00f3ng v\u00e0 hi\u1ec7u qu\u1ea3. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t \u0111\u00e1ng ch\u00fa \u00fd khi gi\u1ea3i lo\u1ea1i ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y:<\/p>\n<p><strong>Ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m:<\/strong> Tr\u01b0\u1eddng h\u1ee3p n\u00e0y x\u1ea3y ra khi c\u00e1c h\u1ec7 s\u1ed1 a, b, c \u0111\u1ec1u c\u00f9ng d\u1ea5u v\u00e0 gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a a nh\u1ecf h\u01a1n gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a c. V\u00ed d\u1ee5: x2+2x+3=0 l\u00e0 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, v\u00ec a, b, c \u0111\u1ec1u d\u01b0\u01a1ng v\u00e0 \u2223a\u2223&lt;\u2223c\u2223 n\u00ean ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng c\u00f3 nghi\u1ec7m th\u1ef1c.<\/p>\n<p><strong>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m:<\/strong> Tr\u01b0\u1eddng h\u1ee3p n\u00e0y x\u1ea3y ra khi t\u1ea5t c\u1ea3 c\u00e1c h\u1ec7 s\u1ed1 a, b, c \u0111\u1ec1u b\u1eb1ng 0. V\u00ed d\u1ee5: 0x2+0x+0=0 l\u00e0 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y th\u00ec m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a x \u0111\u1ec1u l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<p><strong>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m k\u00e9p:<\/strong> Tr\u01b0\u1eddng h\u1ee3p n\u00e0y x\u1ea3y ra khi c\u00e1c h\u1ec7 s\u1ed1 a, b, c th\u1ecfa m\u00e3n m\u1ed9t trong hai \u0111i\u1ec1u ki\u1ec7n: a+b+c=0 ho\u1eb7c a\u2212b+c=0. V\u00ed d\u1ee5: x2\u22125x+6=0 c\u00f3 nghi\u1ec7m k\u00e9p x=3. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y th\u00ec ph\u01b0\u01a1ng tr\u00ecnh nh\u1eadn \u0111\u01b0\u1ee3c ch\u1ec9 c\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t.<\/p>\n<p>Vi\u1ec7c nh\u1eadn bi\u1ebft v\u00e0 x\u1eed l\u00fd c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t n\u00e0y gi\u00fap ch\u00fang ta ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 n\u1ed7 l\u1ef1c trong qu\u00e1 tr\u00ecnh t\u00ecm nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2. Tuy nhi\u00ean, khi kh\u00f4ng th\u1ecfa m\u00e3n c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t, ch\u00fang ta v\u1eabn c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m \u0111\u1ec3 t\u00ecm ra c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x m\u1ed9t c\u00e1ch chi ti\u1ebft v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n<h3>Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ed3 th\u1ecb \u0111\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h3>\n<p>Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ed3 th\u1ecb l\u00e0 m\u1ed9t trong nh\u1eefng c\u00e1ch ti\u1ebfp c\u1eadn ph\u1ed5 bi\u1ebfn \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2. \u0110\u1ec3 \u00e1p d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y, ta c\u1ea7n bi\u1ebft c\u00e1ch v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y=ax^2+bx+c, trong \u0111\u00f3 a, b, c l\u00e0 c\u00e1c h\u1ec7 s\u1ed1 cho tr\u01b0\u1edbc. \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0y c\u00f3 d\u1ea1ng m\u1ed9t Parabol (hay c\u00f2n g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng cong U), c\u00f3 m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb l\u00e0 \u0111\u1ec9nh c\u1ee7a Parabol.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/giai-phuong-trinh-bac-2-6\/\" rel=\"attachment wp-att-297445\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-297445 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6.jpg\" alt=\"giai-phuong-trinh-bac-2-6\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>Khi v\u1ebd \u0111\u1ed3 th\u1ecb, ta c\u1ea7n ch\u00fa \u00fd \u0111\u1ebfn c\u00e1c y\u1ebfu t\u1ed1 sau: \u0110\u1ed9 d\u1ed1c, h\u01b0\u1edbng m\u1edf, t\u00e2m \u0111\u1ed1i x\u1ee9ng v\u00e0 giao \u0111i\u1ec3m v\u1edbi c\u00e1c tr\u1ee5c t\u1ecda \u0111\u1ed9. C\u00e1c giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh y=0 hay n\u00f3i c\u00e1ch kh\u00e1c l\u00e0 c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2.<\/p>\n<p>Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ed3 th\u1ecb c\u00f3 l\u1ee3i th\u1ebf l\u00e0 gi\u00fap ta c\u00f3 c\u00e1i nh\u00ecn t\u1ed5ng qu\u00e1t v\u00e0 sinh \u0111\u1ed9ng v\u1ec1 b\u1ea3n ch\u1ea5t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2, c\u0169ng nh\u01b0 kh\u1ea3 n\u0103ng so s\u00e1nh v\u00e0 ph\u00e2n lo\u1ea1i c\u00e1c tr\u01b0\u1eddng h\u1ee3p c\u00f3 nghi\u1ec7m, v\u00f4 nghi\u1ec7m hay c\u00f3 nghi\u1ec7m k\u00e9p. Tuy nhi\u00ean, ph\u01b0\u01a1ng ph\u00e1p n\u00e0y c\u0169ng g\u1eb7p ph\u1ea3i m\u1ed9t s\u1ed1 h\u1ea1n ch\u1ebf nh\u01b0 sai s\u1ed1 do qu\u00e1 tr\u00ecnh v\u1ebd \u0111\u1ed3 th\u1ecb kh\u00f4ng th\u1ec3 ho\u00e0n to\u00e0n ch\u00ednh x\u00e1c, ph\u1ee5 thu\u1ed9c v\u00e0o k\u1ef9 n\u0103ng v\u00e0 c\u00f4ng c\u1ee5 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a ng\u01b0\u1eddi gi\u1ea3i v\u00e0 kh\u00f3 kh\u0103n trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh nghi\u1ec7m ch\u00ednh x\u00e1c. Nh\u1eefng kh\u00f3 kh\u0103n n\u00e0y hay x\u1ea3y ra khi \u0111\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c ho\u00e0nh \u1edf nh\u1eefng \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 l\u00e0 c\u00e1c s\u1ed1 th\u1eadp ph\u00e2n, ph\u00e2n s\u1ed1 hay s\u1ed1 c\u0103n.<\/p>\n<h3>Ph\u01b0\u01a1ng ph\u00e1p nh\u1ea9m nghi\u1ec7m<\/h3>\n<p>\u0110\u00e2y l\u00e0 ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 d\u1ef1a tr\u00ean vi\u1ec7c nh\u1eadn bi\u1ebft m\u1ed9t s\u1ed1 d\u1ea1ng \u0111\u1eb7c bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2. N\u00f3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng theo m\u1ed9t \u0111\u1ecbnh l\u00fd quen thu\u1ed9c, \u0111\u00f3 ch\u00ednh l\u00e0 \u0111\u1ecbnh l\u00fd Vi-et. Ph\u01b0\u01a1ng ph\u00e1p nghi\u1ec7m l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p nh\u1ea9m nhanh \u0111\u01b0\u1ee3c nghi\u1ec7m m\u00e0 kh\u00f4ng c\u1ea7n s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m. M\u1ed9t s\u1ed1 d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u00f3 th\u1ec3 nh\u1ea9m nghi\u1ec7m nh\u01b0 sau:<\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng ax^2 + bx + c = 0 v\u1edbi a + b + c = 0. Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y s\u1ebd c\u00f3 nghi\u1ec7m x1 = 1 v\u00e0 x2 = c\/a.<\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng ax^2 + bx + c = 0 v\u1edbi a &#8211; b + c = 0. Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y s\u1ebd c\u00f3 nghi\u1ec7m x1 = -1 v\u00e0 x2 = -c\/a.<\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng ax^2 + (a + b)x + b = 0. Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y s\u1ebd c\u00f3 nghi\u1ec7m x1 = -1 v\u00e0 x2 = -b\/a.<\/p>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng x^2 + px + q = 0 v\u1edbi p, q l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean v\u00e0 q chia h\u1ebft cho p. Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y s\u1ebd c\u00f3 nghi\u1ec7m x1 = -p v\u00e0 x2 = -q\/p.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/giai-phuong-trinh-bac-2-7\/\" rel=\"attachment wp-att-297446\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-297446 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7.jpg\" alt=\"giai-phuong-trinh-bac-2-7\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>Ph\u01b0\u01a1ng ph\u00e1p nh\u1ea9m nghi\u1ec7m gi\u00fap ta gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 m\u1ed9t c\u00e1ch nhanh ch\u00f3ng v\u00e0 thu\u1eadn ti\u1ec7n khi c\u00e1c d\u1ea1ng \u0111\u1eb7c bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c nh\u1eadn bi\u1ebft v\u00e0 \u00e1p d\u1ee5ng. Tuy nhi\u00ean, n\u00f3 ch\u1ec9 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c cho m\u1ed9t s\u1ed1 d\u1ea1ng c\u1ee5 th\u1ec3 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 kh\u00f4ng th\u1ec3 s\u1eed d\u1ee5ng cho t\u1ea5t c\u1ea3 c\u00e1c tr\u01b0\u1eddng h\u1ee3p.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p><span style=\"font-weight: 400;\">T\u00f3m t\u1eaft: C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 x = [-b \u00b1 \u221a\u0394]\/2a (\u0394 = b\u00b2 &#8211; 4ac). \u00c1p d\u1ee5ng linh ho\u1ea1t cho To\u00e1n l\u1edbp 9: \u0394 &gt; 0 (2 nghi\u1ec7m), \u0394 = 0 (nghi\u1ec7m k\u00e9p), \u0394 &lt; 0 (v\u00f4 nghi\u1ec7m). Luy\u1ec7n th\u00eam b\u00e0i t\u1eadp Viet v\u00e0 nghi\u1ec7m thu g\u1ecdn \u0111\u1ec3 master ki\u1ebfn th\u1ee9c<\/span><\/p>\n<p>Xem th\u00eam:<\/p>\n<ul>\n<li class=\"elementor-heading-title elementor-size-default\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dau-hieu-nhan-biet-tu-giac-noi-tiep\/\">D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp v\u00e0 v\u00ed d\u1ee5 minh ho\u1ea1<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/c\/\">C++ l\u00e0 g\u00ec? T\u1ed5ng h\u1ee3p ki\u1ebfn th\u1ee9c h\u1ecdc C++ c\u01a1 b\u1ea3n c\u1ef1c d\u1ec5 hi\u1ec3u<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (a \u2260 0) l\u00e0 x = [-b \u00b1 \u221a\u0394] \/ (2a), v\u1edbi \u0394 = b\u00b2 &#8211; 4ac l\u00e0 bi\u1ec7t th\u1ee9c. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c c\u1ed1t l\u00f5i To\u00e1n l\u1edbp 9, gi\u00fap gi\u1ea3i nhanh m\u1ecdi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn [&hellip;]<\/p>\n","protected":false},"author":86,"featured_media":297440,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-297425","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 | To\u00e1n l\u1edbp 9 chi ti\u1ebft<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2: x = [-b \u00b1 \u221a(b\u00b2 - 4ac)] \/ 2a. H\u01b0\u1edbng d\u1eabn chi ti\u1ebft \u0394 = b\u00b2 - 4ac, nghi\u1ec7m k\u00e9p, hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, v\u00f4 nghi\u1ec7m. V\u00ed d\u1ee5 To\u00e1n l\u1edbp 9 d\u1ec5 hi\u1ec3u, b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (To\u00e1n l\u1edbp 9)\" \/>\n<meta property=\"og:description\" content=\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2: x = [-b \u00b1 \u221a(b\u00b2 - 4ac)] \/ 2a. H\u01b0\u1edbng d\u1eabn chi ti\u1ebft \u0394 = b\u00b2 - 4ac, nghi\u1ec7m k\u00e9p, hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, v\u00f4 nghi\u1ec7m. V\u00ed d\u1ee5 To\u00e1n l\u1edbp 9 d\u1ec5 hi\u1ec3u, b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:published_time\" content=\"2023-12-19T04:35:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-20T07:50:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"C\u00f9 Ho\u00e0ng T\u00e2m\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"C\u00f9 Ho\u00e0ng T\u00e2m\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"13 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\"},\"author\":{\"name\":\"C\u00f9 Ho\u00e0ng T\u00e2m\",\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/c713452346275d296df23ce2d1aa2a9b\"},\"headline\":\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (To\u00e1n l\u1edbp 9)\",\"datePublished\":\"2023-12-19T04:35:21+00:00\",\"dateModified\":\"2025-12-20T07:50:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\"},\"wordCount\":3004,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/#organization\"},\"image\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-1.jpg\",\"articleSection\":[\"Kh\u00e1m Ph\u00e1\",\"Ki\u1ebfn Th\u1ee9c\"],\"inLanguage\":\"vi\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/#respond\"]}],\"copyrightYear\":\"2023\",\"copyrightHolder\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\",\"url\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/\",\"name\":\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 | To\u00e1n l\u1edbp 9 chi ti\u1ebft\",\"isPartOf\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/giai-phuong-trinh-bac-2\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-1.jpg\",\"datePublished\":\"2023-12-19T04:35:21+00:00\",\"dateModified\":\"2025-12-20T07:50:18+00:00\",\"description\":\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2: x = [-b \u00b1 \u221a(b\u00b2 - 4ac)] \/ 2a. 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