{"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":"2026-11-05T14:03:14","modified_gmt":"2026-11-05T07:03:14","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><strong>C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (a \u2260 0) l\u00e0 x = (\u2212b \u00b1 \u221a\u0394) \/ (2a), v\u1edbi bi\u1ec7t th\u1ee9c \u0394 = b\u00b2 \u2212 4ac.<\/strong> N\u1ebfu \u0394 > 0 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, \u0394 = 0 c\u00f3 nghi\u1ec7m k\u00e9p x = \u2212b \/ (2a), \u0394 < 0 v\u00f4 nghi\u1ec7m (trong t\u1eadp s\u1ed1 th\u1ef1c). \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a To\u00e1n l\u1edbp 9. B\u00e0i vi\u1ebft tr\u00ecnh b\u00e0y c\u00f4ng th\u1ee9c nghi\u1ec7m, c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn, c\u00e1ch nh\u1ea9m nghi\u1ec7m, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh khuy\u1ebft v\u00e0 v\u00ed d\u1ee5 gi\u1ea3i t\u1eebng b\u01b0\u1edbc.<\/p>\n<p><strong>T\u00f3m t\u1eaft nhanh:<\/strong><\/p>\n<ul>\n<li><strong>T\u00ednh \u0394:<\/strong> \u0394 = b\u00b2 \u2212 4ac.<\/li>\n<li><strong>\u0394 > 0:<\/strong> x\u2081 = (\u2212b + \u221a\u0394) \/ 2a, x\u2082 = (\u2212b \u2212 \u221a\u0394) \/ 2a. <strong>\u0394 = 0:<\/strong> x = \u2212b \/ 2a. <strong>\u0394 < 0:<\/strong> v\u00f4 nghi\u1ec7m.<\/li>\n<li><strong>b ch\u1eb5n (b = 2b&#8217;):<\/strong> d\u00f9ng \u0394&#8217; = b&#8217;\u00b2 \u2212 ac, x = (\u2212b&#8217; \u00b1 \u221a\u0394&#8217;) \/ a.<\/li>\n<li><strong>Nh\u1ea9m nhanh:<\/strong> a + b + c = 0 th\u00ec x\u2081 = 1, x\u2082 = c\/a; a \u2212 b + c = 0 th\u00ec x\u2081 = \u22121, x\u2082 = \u2212c\/a.<\/li>\n<\/ul>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-297441\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-2.jpg\" alt=\"Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 d\u1ea1ng t\u1ed5ng qu\u00e1t v\u00e0 c\u00f4ng th\u1ee9c nghi\u1ec7m\" 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\" \/><\/p>\n<h2>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 g\u00ec?<\/h2>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 m\u1ed9t \u1ea9n l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng <strong>ax\u00b2 + bx + c = 0<\/strong>, trong \u0111\u00f3 x l\u00e0 \u1ea9n, a, b, c l\u00e0 c\u00e1c s\u1ed1 \u0111\u00e3 bi\u1ebft v\u00e0 <strong>a \u2260 0<\/strong>. H\u1ec7 s\u1ed1 a \u0111\u1ee9ng tr\u01b0\u1edbc x\u00b2, b \u0111\u1ee9ng tr\u01b0\u1edbc x, c l\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do. N\u1ebfu a = 0, ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng c\u00f2n l\u00e0 b\u1eadc 2 m\u00e0 tr\u1edf th\u00e0nh ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t bx + c = 0.<\/p>\n<p>V\u00ed d\u1ee5: x\u00b2 \u2212 5x + 6 = 0 (a = 1, b = \u22125, c = 6); 2x\u00b2 \u2212 8 = 0 (a = 2, b = 0, c = \u22128); 3x\u00b2 \u2212 6x = 0 (a = 3, b = \u22126, c = 0).<\/p>\n<h2>C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h2>\n<p>V\u1edbi ph\u01b0\u01a1ng tr\u00ecnh ax\u00b2 + bx + c = 0 (a \u2260 0), t\u00ednh bi\u1ec7t th\u1ee9c:<\/p>\n<p style=\"text-align: center;\"><strong>\u0394 = b\u00b2 \u2212 4ac<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>Gi\u00e1 tr\u1ecb \u0394<\/th>\n<th>K\u1ebft lu\u1eadn<\/th>\n<th>Nghi\u1ec7m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0394 > 0<\/td>\n<td>Hai nghi\u1ec7m ph\u00e2n bi\u1ec7t<\/td>\n<td>x\u2081 = (\u2212b + \u221a\u0394) \/ (2a); x\u2082 = (\u2212b \u2212 \u221a\u0394) \/ (2a)<\/td>\n<\/tr>\n<tr>\n<td>\u0394 = 0<\/td>\n<td>Nghi\u1ec7m k\u00e9p<\/td>\n<td>x\u2081 = x\u2082 = \u2212b \/ (2a)<\/td>\n<\/tr>\n<tr>\n<td>\u0394 < 0<\/td>\n<td>V\u00f4 nghi\u1ec7m (trong t\u1eadp s\u1ed1 th\u1ef1c)<\/td>\n<td>Kh\u00f4ng c\u00f3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0394 \u00e2m th\u00ec kh\u00f4ng l\u1ea5y \u0111\u01b0\u1ee3c c\u0103n b\u1eadc hai trong t\u1eadp s\u1ed1 th\u1ef1c, \u0111\u00f3 l\u00e0 l\u00fd do ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m; xem th\u00eam b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/can-bac-hai-la-gi\/\">c\u0103n b\u1eadc hai<\/a>. \u00dd ngh\u0129a v\u00e0 c\u00e1ch d\u00f9ng bi\u1ec7t th\u1ee9c \u0111\u01b0\u1ee3c gi\u1ea3i th\u00edch ri\u00eang trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/delta-delta-phay\/\">c\u00f4ng th\u1ee9c delta v\u00e0 delta ph\u1ea9y<\/a>.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-297442\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-3.jpg\" alt=\"C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 x = (-b \u00b1 \u221a(b\u00b2 - 4ac)) \/ 2a\" 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\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn (khi b ch\u1eb5n)<\/h2>\n<p>Khi b = 2b&#8217; (b ch\u1eb5n ho\u1eb7c c\u00f3 d\u1ea1ng 2 nh\u00e2n m\u1ed9t bi\u1ec3u th\u1ee9c), d\u00f9ng c\u00f4ng th\u1ee9c thu g\u1ecdn \u0111\u1ec3 t\u00ednh nhanh h\u01a1n:<\/p>\n<p style=\"text-align: center;\"><strong>\u0394&#8217; = b&#8217;\u00b2 \u2212 ac<\/strong><\/p>\n<ul>\n<li>\u0394&#8217; > 0: x\u2081 = (\u2212b&#8217; + \u221a\u0394&#8217;) \/ a; x\u2082 = (\u2212b&#8217; \u2212 \u221a\u0394&#8217;) \/ a.<\/li>\n<li>\u0394&#8217; = 0: nghi\u1ec7m k\u00e9p x = \u2212b&#8217; \/ a.<\/li>\n<li>\u0394&#8217; < 0: v\u00f4 nghi\u1ec7m.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5: x\u00b2 \u2212 6x + 5 = 0 c\u00f3 b&#8217; = \u22123, \u0394&#8217; = 9 \u2212 5 = 4, \u221a\u0394&#8217; = 2, n\u00ean x\u2081 = 3 + 2 = 5, x\u2082 = 3 \u2212 2 = 1.<\/p>\n<h2>C\u00e1c b\u01b0\u1edbc gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 b\u1eb1ng c\u00f4ng th\u1ee9c nghi\u1ec7m<\/h2>\n<ol>\n<li><strong>X\u00e1c \u0111\u1ecbnh a, b, c<\/strong> (ch\u00fa \u00fd d\u1ea5u). V\u1edbi x\u00b2 \u2212 5x + 6 = 0: a = 1, b = \u22125, c = 6.<\/li>\n<li><strong>T\u00ednh \u0394<\/strong> = b\u00b2 \u2212 4ac = 25 \u2212 24 = 1.<\/li>\n<li><strong>X\u00e9t d\u1ea5u \u0394:<\/strong> \u0394 = 1 > 0 n\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t.<\/li>\n<li><strong>T\u00ednh nghi\u1ec7m:<\/strong> x\u2081 = (5 + 1) \/ 2 = 3; x\u2082 = (5 \u2212 1) \/ 2 = 2.<\/li>\n<li><strong>Th\u1eed l\u1ea1i<\/strong> (n\u00ean l\u00e0m): 3\u00b2 \u2212 5\u00b73 + 6 = 0 v\u00e0 2\u00b2 \u2212 5\u00b72 + 6 = 0.<\/li>\n<\/ol>\n<h2>V\u00ed d\u1ee5 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p><strong>V\u00ed d\u1ee5 1 (\u0394 > 0):<\/strong> Gi\u1ea3i 6x\u00b2 \u2212 17x + 12 = 0.<br \/>\u0394 = (\u221217)\u00b2 \u2212 4\u00b76\u00b712 = 289 \u2212 288 = 1. x\u2081 = (17 + 1) \/ 12 = 3\/2; x\u2082 = (17 \u2212 1) \/ 12 = 4\/3.<\/p>\n<p><strong>V\u00ed d\u1ee5 2 (\u0394 = 0):<\/strong> Gi\u1ea3i x\u00b2 \u2212 4x + 4 = 0.<br \/>\u0394 = 16 \u2212 16 = 0, ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m k\u00e9p x = 4 \/ 2 = 2.<\/p>\n<p><strong>V\u00ed d\u1ee5 3 (\u0394 < 0):<\/strong> Gi\u1ea3i x\u00b2 + 2x + 3 = 0.<br \/>\u0394 = 4 \u2212 12 = \u22128 < 0, ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m.<\/p>\n<p><strong>V\u00ed d\u1ee5 4 (hai nghi\u1ec7m v\u00f4 t\u1ec9):<\/strong> Gi\u1ea3i x\u00b2 + 5x + 2 = 0.<br \/>\u0394 = 25 \u2212 8 = 17 > 0. x\u2081 = (\u22125 + \u221a17) \/ 2, x\u2082 = (\u22125 \u2212 \u221a17) \/ 2 (x\u1ea5p x\u1ec9 \u22120,44 v\u00e0 \u22124,56).<\/p>\n<h2>C\u00e1ch nh\u1ea9m nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 b\u1eb1ng \u0111\u1ecbnh l\u00fd Vi-\u00e9t<\/h2>\n<p>N\u1ebfu ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m x\u2081, x\u2082 th\u00ec theo \u0111\u1ecbnh l\u00fd Vi-\u00e9t: <strong>x\u2081 + x\u2082 = \u2212b\/a<\/strong> v\u00e0 <strong>x\u2081 \u00b7 x\u2082 = c\/a<\/strong>. T\u1eeb \u0111\u00f3 c\u00f3 c\u00e1c tr\u01b0\u1eddng h\u1ee3p nh\u1ea9m nghi\u1ec7m nhanh:<\/p>\n<table>\n<thead>\n<tr>\n<th>D\u1ea5u hi\u1ec7u<\/th>\n<th>Nghi\u1ec7m<\/th>\n<th>V\u00ed d\u1ee5<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>a + b + c = 0<\/td>\n<td>x\u2081 = 1, x\u2082 = c\/a<\/td>\n<td>3x\u00b2 \u2212 7x + 4 = 0 \u2192 x = 1; x = 4\/3<\/td>\n<\/tr>\n<tr>\n<td>a \u2212 b + c = 0<\/td>\n<td>x\u2081 = \u22121, x\u2082 = \u2212c\/a<\/td>\n<td>2x\u00b2 \u2212 3x \u2212 5 = 0 \u2192 x = \u22121; x = 5\/2<\/td>\n<\/tr>\n<tr>\n<td>T\u00ecm hai s\u1ed1 c\u00f3 t\u1ed5ng S, t\u00edch P<\/td>\n<td>L\u00e0 nghi\u1ec7m c\u1ee7a x\u00b2 \u2212 Sx + P = 0<\/td>\n<td>T\u1ed5ng 7, t\u00edch 12 \u2192 x\u00b2 \u2212 7x + 12 = 0 \u2192 3 v\u00e0 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>L\u01b0u \u00fd: ch\u1ec9 nh\u1ea9m \u0111\u01b0\u1ee3c khi ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng \u0111\u1eb7c bi\u1ec7t; c\u00e1c tr\u01b0\u1eddng h\u1ee3p c\u00f2n l\u1ea1i v\u1eabn d\u00f9ng c\u00f4ng th\u1ee9c nghi\u1ec7m.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-297446\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-7.jpg\" alt=\"C\u00e1ch nh\u1ea9m nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 theo \u0111\u1ecbnh l\u00fd Vi-\u00e9t\" 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\" \/><\/p>\n<h2>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 khuy\u1ebft b ho\u1eb7c khuy\u1ebft c<\/h2>\n<ul>\n<li><strong>Khuy\u1ebft c (c = 0):<\/strong> \u0111\u1eb7t nh\u00e2n t\u1eed chung. V\u00ed d\u1ee5 3x\u00b2 \u2212 6x = 0 \u21d4 3x(x \u2212 2) = 0 \u21d4 x = 0 ho\u1eb7c x = 2.<\/li>\n<li><strong>Khuy\u1ebft b (b = 0):<\/strong> chuy\u1ec3n v\u1ebf r\u1ed3i l\u1ea5y c\u0103n. V\u00ed d\u1ee5 2x\u00b2 \u2212 8 = 0 \u21d4 x\u00b2 = 4 \u21d4 x = 2 ho\u1eb7c x = \u22122. N\u1ebfu x\u00b2 b\u1eb1ng s\u1ed1 \u00e2m th\u00ec ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m.<\/li>\n<\/ul>\n<h2>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 b\u1eb1ng \u0111\u1ed3 th\u1ecb<\/h2>\n<p>Nghi\u1ec7m c\u1ee7a ax\u00b2 + bx + c = 0 l\u00e0 ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a parabol y = ax\u00b2 + bx + c v\u1edbi tr\u1ee5c ho\u00e0nh. V\u00ed d\u1ee5 \u0111\u1ed3 th\u1ecb y = x\u00b2 \u2212 4x c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i x = 0 v\u00e0 x = 4, \u0111\u1ec9nh parabol l\u00e0 (2; \u22124). C\u00e1ch v\u1ebd \u0111\u1ed3 th\u1ecb c\u00f3 trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-bac-2-la-gi\/\">h\u00e0m s\u1ed1 b\u1eadc 2<\/a>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-297445\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/giai-phuong-trinh-bac-2-6.jpg\" alt=\"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 b\u1eb1ng \u0111\u1ed3 th\u1ecb parabol y = x\u00b2 - 4x\" 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\" \/><\/p>\n<p>C\u00e1ch n\u00e0y gi\u00fap h\u00ecnh dung s\u1ed1 nghi\u1ec7m (parabol c\u1eaft, ti\u1ebfp x\u00fac hay kh\u00f4ng c\u1eaft tr\u1ee5c ho\u00e0nh) nh\u01b0ng kh\u00f3 cho nghi\u1ec7m ch\u00ednh x\u00e1c khi nghi\u1ec7m l\u00e0 ph\u00e2n s\u1ed1 ho\u1eb7c s\u1ed1 v\u00f4 t\u1ec9.<\/p>\n<h2>L\u1ed7i th\u01b0\u1eddng g\u1eb7p khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/h2>\n<ul>\n<li>L\u1ea5y sai d\u1ea5u c\u1ee7a b, c (v\u00ed d\u1ee5 x\u00b2 \u2212 5x + 6 = 0 th\u00ec b = \u22125, kh\u00f4ng ph\u1ea3i 5).<\/li>\n<li>Qu\u00ean \u0111i\u1ec1u ki\u1ec7n a \u2260 0 khi ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a tham s\u1ed1.<\/li>\n<li>Ch\u1ec9 chia \u221a\u0394 cho 2a thay v\u00ec chia c\u1ea3 t\u1eed s\u1ed1 (\u2212b \u00b1 \u221a\u0394).<\/li>\n<li>D\u00f9ng c\u00f4ng th\u1ee9c thu g\u1ecdn nh\u01b0ng v\u1eabn chia cho 2a thay v\u00ec chia cho a.<\/li>\n<\/ul>\n<p>C\u00f3 th\u1ec3 ki\u1ec3m tra \u0111\u00e1p \u00e1n b\u1eb1ng m\u00e1y t\u00ednh c\u1ea7m tay, xem b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/may-tinh-580\/\">m\u00e1y t\u00ednh Casio fx-580VN X<\/a>.<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p<\/h2>\n<h3>C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 g\u00ec?<\/h3>\n<p>V\u1edbi ax\u00b2 + bx + c = 0 (a \u2260 0), t\u00ednh \u0394 = b\u00b2 \u2212 4ac; n\u1ebfu \u0394 \u2265 0 th\u00ec x = (\u2212b \u00b1 \u221a\u0394) \/ (2a), n\u1ebfu \u0394 < 0 th\u00ec ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m.<\/p>\n<h3>Khi n\u00e0o ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u00f3 nghi\u1ec7m k\u00e9p?<\/h3>\n<p>Khi \u0394 = b\u00b2 \u2212 4ac = 0. Khi \u0111\u00f3 nghi\u1ec7m k\u00e9p l\u00e0 x = \u2212b \/ (2a), v\u00ed d\u1ee5 x\u00b2 \u2212 4x + 4 = 0 c\u00f3 nghi\u1ec7m k\u00e9p x = 2.<\/p>\n<h3>Khi n\u00e0o ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 v\u00f4 nghi\u1ec7m?<\/h3>\n<p>Khi \u0394 = b\u00b2 \u2212 4ac < 0, v\u00ed d\u1ee5 x\u00b2 + 2x + 3 = 0 c\u00f3 \u0394 = \u22128 n\u00ean v\u00f4 nghi\u1ec7m trong t\u1eadp s\u1ed1 th\u1ef1c.<\/p>\n<h3>Khi n\u00e0o d\u00f9ng c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn?<\/h3>\n<p>Khi h\u1ec7 s\u1ed1 b ch\u1eb5n (b = 2b&#8217;). Khi \u0111\u00f3 \u0394&#8217; = b&#8217;\u00b2 \u2212 ac v\u00e0 x = (\u2212b&#8217; \u00b1 \u221a\u0394&#8217;) \/ a, gi\u00fap t\u00ednh nhanh v\u00e0 \u00edt sai h\u01a1n.<\/p>\n<h3>Nh\u1ea9m nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 th\u1ebf n\u00e0o?<\/h3>\n<p>N\u1ebfu a + b + c = 0 th\u00ec hai nghi\u1ec7m l\u00e0 1 v\u00e0 c\/a; n\u1ebfu a \u2212 b + c = 0 th\u00ec hai nghi\u1ec7m l\u00e0 \u22121 v\u00e0 \u2212c\/a.<\/p>\n<h3>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 h\u1ecdc \u1edf l\u1edbp m\u1ea5y?<\/h3>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 m\u1ed9t \u1ea9n, c\u00f4ng th\u1ee9c nghi\u1ec7m v\u00e0 \u0111\u1ecbnh l\u00fd Vi-\u00e9t thu\u1ed9c ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 9.<\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"V\u1edbi ax\u00b2 + bx + c = 0 (a \u2260 0), t\u00ednh \u0394 = b\u00b2 \u2212 4ac; n\u1ebfu \u0394 \u2265 0 th\u00ec x = (\u2212b \u00b1 \u221a\u0394) \/ (2a), n\u1ebfu \u0394 < 0 th\u00ec ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Khi n\u00e0o ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u00f3 nghi\u1ec7m k\u00e9p?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Khi \u0394 = b\u00b2 \u2212 4ac = 0. Khi \u0111\u00f3 nghi\u1ec7m k\u00e9p l\u00e0 x = \u2212b \/ (2a), v\u00ed d\u1ee5 x\u00b2 \u2212 4x + 4 = 0 c\u00f3 nghi\u1ec7m k\u00e9p x = 2.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Khi n\u00e0o ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 v\u00f4 nghi\u1ec7m?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Khi \u0394 = b\u00b2 \u2212 4ac < 0, v\u00ed d\u1ee5 x\u00b2 + 2x + 3 = 0 c\u00f3 \u0394 = \u22128 n\u00ean v\u00f4 nghi\u1ec7m trong t\u1eadp s\u1ed1 th\u1ef1c.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Khi n\u00e0o d\u00f9ng c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Khi h\u1ec7 s\u1ed1 b ch\u1eb5n (b = 2b'). Khi \u0111\u00f3 \u0394' = b'\u00b2 \u2212 ac v\u00e0 x = (\u2212b' \u00b1 \u221a\u0394') \/ a, gi\u00fap t\u00ednh nhanh v\u00e0 \u00edt sai h\u01a1n.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Nh\u1ea9m nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"N\u1ebfu a + b + c = 0 th\u00ec hai nghi\u1ec7m l\u00e0 1 v\u00e0 c\/a; n\u1ebfu a \u2212 b + c = 0 th\u00ec hai nghi\u1ec7m l\u00e0 \u22121 v\u00e0 \u2212c\/a.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 h\u1ecdc \u1edf l\u1edbp m\u1ea5y?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 m\u1ed9t \u1ea9n, c\u00f4ng th\u1ee9c nghi\u1ec7m v\u00e0 \u0111\u1ecbnh l\u00fd Vi-\u00e9t thu\u1ed9c ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 9.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>\u0110\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0, h\u00e3y x\u00e1c \u0111\u1ecbnh \u0111\u00fang a, b, c, t\u00ednh \u0394 = b\u00b2 \u2212 4ac r\u1ed3i k\u1ebft lu\u1eadn theo d\u1ea5u c\u1ee7a \u0394; khi b ch\u1eb5n, d\u00f9ng \u0394' cho g\u1ecdn, v\u00e0 lu\u00f4n th\u1eed nh\u1ea9m nghi\u1ec7m theo a + b + c ho\u1eb7c a \u2212 b + c tr\u01b0\u1edbc. Khi \u0111\u00e3 th\u00e0nh th\u1ea1o, b\u1ea1n c\u00f3 th\u1ec3 h\u1ecdc ti\u1ebfp <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/he-phuong-trinh\/\">h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/a> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/parabol\/\">parabol<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 ax\u00b2 + bx + c = 0 (a \u2260 0) l\u00e0 x = (\u2212b \u00b1 \u221a\u0394) \/ (2a), v\u1edbi bi\u1ec7t th\u1ee9c \u0394 = b\u00b2 \u2212 4ac. N\u1ebfu \u0394 > 0 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, \u0394 = 0 c\u00f3 nghi\u1ec7m k\u00e9p x = \u2212b \/ [&hellip;]<\/p>\n","protected":false},"author":86,"featured_media":297440,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2","_yoast_wpseo_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","_yoast_wpseo_metadesc":"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.","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 v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\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. 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