Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
\u0110a th\u1ee9c m\u1ed9t bi\u1ebfn l\u00e0 m\u1ed9t trong nh\u1eefng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 l\u00e0 d\u1ea1ng to\u00e1n \u0111i\u1ec3n h\u00ecnh trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u1ecdc l\u1edbp 7. \u0110\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c d\u1ea1ng to\u00e1n n\u00e0y c\u1ea7n n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft c\u0169ng nh\u01b0 c\u00e1ch t\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn. Ch\u00ednh v\u00ec v\u1eady Vietlearn.org\/ s\u1ebd cung c\u1ea5p ki\u1ebfn th\u1ee9c \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t cho c\u00e1c em h\u1ecdc sinh<\/a> qua b\u00e0i gi\u1ea3ng sau.<\/p>\n\n\n\n N\u1ed9i dung b\u00e0i gi\u1ea3ng t\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn<\/p>\n\n\n\n I. L\u00fd thuy\u1ebft nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn<\/p>\n\n\n\n Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u v\u1ec1 tr\u1ecdng t\u00e2m c\u1ee7a b\u00e0i vi\u1ebft h\u00f4m nay, ch\u00fang ta s\u1ebd n\u00f3i qua v\u1ec1 d\u1ea1ng \u0111a th\u1ee9c 1 bi\u1ebfn. V\u1ec1 c\u01a1 b\u1ea3n, t\u1ed5ng c\u1ee7a nh\u1eefng \u0111\u01a1n th\u1ee9c trong c\u00f9ng 1 bi\u1ebfn s\u1ebd \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a th\u1ee9c 1 bi\u1ebfn. Ngo\u00e0i ra m\u1ed7i s\u1ed1 s\u1ebd \u0111\u01b0\u1ee3c coi nh\u01b0 l\u00e0 m\u1ed9t \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn. Th\u00f4ng th\u01b0\u1eddng gi\u00e1 tr\u1ecb c\u1ee7a \u0111a th\u1ee9c P(x) m\u1ed9t bi\u1ebfn t\u1ea1i x = a trong to\u00e1n h\u1ecdc s\u1ebd k\u00ed hi\u1ec7u l\u00e0 P(x)<\/p>\n\n\n\n V\u00ed d\u1ee5 minh h\u1ecda: Cho \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn P(x) = 3×3 + 2×2 \u2013 x + 1<\/p>\n\n\n\n V\u1edbi x = 2 ta c\u00f3 P(2) = 3.23 + 2.22 \u2013 2 + 1 = 31<\/p>\n\n\n\n Trong h\u1ec7 s\u1ed1 \u0111a th\u1ee9c h\u1ec7 s\u1ed1 t\u1ef1 do ch\u00ednh l\u00e0 s\u1ed1 h\u1ea1ng m\u00e0 kh\u00f4ng ch\u1ee9a bi\u1ebfn v\u00e0 h\u1ec7 s\u1ed1 cao nh\u1ea5t s\u1ebd l\u00e0 h\u1ec7 s\u1ed1 c\u1ee7a ch\u00ednh s\u1ed1 h\u1ea1ng c\u00f3 b\u1eadc cao nh\u1ea5t.<\/p>\n\n\n\n \u0110a th\u1ee9c m\u1ed9t bi\u1ebfn<\/p><\/blockquote>\n\n\n\n Cho \u0111a th\u1ee9c P(x) sau:<\/p>\n\n\n\n N\u1ebfu t\u1ea1i x = a l\u00e0m cho \u0111a th\u1ee9c P(x) \u0111\u00e3 cho c\u00f3 gi\u00e1 tr\u1ecb = 0 th\u00ec a ch\u00ednh l\u00e0 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c P(x) \u0111\u00f3<\/p>\n\n\n\n Kh\u00e1i ni\u1ec7m nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn<\/p>\n\n\n\n Nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn l\u1edbp 7 l\u00e0 m\u1ed9t trong nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng quan tr\u1ecdng c\u1ea7n ph\u1ea3i n\u1eafm. Theo \u0111\u00f3 m\u1ed9t \u0111a th\u1ee9c c\u00f3 th\u1ec3 c\u00f3 t\u1edbi 1, 2, 3,\u2026 ho\u1eb7c n nghi\u1ec7m. Ngo\u00e0i ra \u0111a th\u1ee9c c\u0169ng c\u00f3 th\u1ec3 kh\u00f4ng c\u00f3 nghi\u1ec7m n\u00e0o. Tuy nhi\u00ean \u0111\u00f3 ph\u1ea3i l\u00e0 \u0111a th\u1ee9c kh\u00e1c v\u1edbi \u0111a th\u1ee9c kh\u00f4ng.<\/p>\n\n\n\n L\u01b0u \u00fd:<\/p>\n\n\n\n M\u1ed9t trong nh\u1eefng l\u01b0u \u00fd quan tr\u1ecdng khi t\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn \u0111\u00f3 ch\u00ednh l\u00e0 s\u1ed1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c \u0111\u00f3 (kh\u00e1c v\u1edbi \u0111a th\u1ee9c 0) b\u1eaft bu\u1ed9c kh\u00f4ng \u0111\u01b0\u1ee3c v\u01b0\u1ee3t qu\u00e1 b\u1eadc c\u1ee7a n\u00f3.<\/p>\n\n\n\n Theo l\u00fd thuy\u1ebft, nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn l\u00e0 a n\u1ebfu thay x = a l\u00e0m cho \u0111a th\u1ee9c P(x) \u0111\u00e3 cho c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng 0<\/p>\n\n\n\n Do \u0111\u00f3 c\u00e1ch t\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn l\u00e0 cho \u0111a th\u1ee9c \u0111\u00f3 = 0 sau \u0111\u00f3 gi\u1ea3i nh\u01b0 ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n b\u00ecnh th\u01b0\u1eddng.<\/p>\n\n\n\n V\u00ed d\u1ee5 minh h\u1ecda:<\/p>\n\n\n\n Cho \u0111a th\u1ee9c sau P(x) = 2x \u2013 8. T\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho tr\u00ean<\/p>\n\n\n\n H\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft:<\/p>\n\n\n\n Ta c\u00f3: P(x) = 0 <=> 2x \u2013 8 = 0 <=> x = 4.<\/p>\n\n\n\n V\u1eady nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn P(x) = 0 l\u00e0 x = 4<\/p>\n\n\n\n II. C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn:<\/p>\n\n\n\n D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m v\u1ec1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn sau s\u1ebd gi\u00fap c\u00e1c em h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 d\u1ec5 d\u00e0ng gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c b\u00e0i ki\u1ec3m tra nhanh nhanh ch\u00f3ng nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp tr\u1eafc nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn<\/p>\n\n\n\n B\u00e0i t\u1eadp 1: L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<\/p>\n\n\n\n Cho \u0111a th\u1ee9c sau: f(x) = x2 + 6x + 8. \u0110\u00e2u l\u00e0 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho tr\u00ean:<\/p>\n\n\n\n C\u00e2u A: 7<\/p>\n\n\n\n C\u00e2u B: 6<\/p>\n\n\n\n C\u00e2u C: 5<\/p>\n\n\n\n C\u00e2u D: 4<\/p>\n\n\n\n B\u00e0i t\u1eadp 2: L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<\/p>\n\n\n\n Cho \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn sau: x3 + 8. S\u1ed1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho l\u00e0.<\/p>\n\n\n\n C\u00e2u A: 3<\/p>\n\n\n\n C\u00e2u B: 2<\/p>\n\n\n\n C\u00e2u C: 1<\/p>\n\n\n\n C\u00e2u D: 0<\/p>\n\n\n\n B\u00e0i t\u1eadp 3: L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<\/p>\n\n\n\n Cho \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn sau: 3×2 \u2013 27. Hi\u1ec7u s\u1ed1 gi\u1eefa nghi\u1ec7m l\u1edbn nh\u1ea5t v\u00e0 nghi\u1ec7m nh\u1ecf nh\u1ea5t c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn \u0111\u00e3 cho l\u00e0:<\/p>\n\n\n\n C\u00e2u A: -1<\/p>\n\n\n\n C\u00e2u B: -6<\/p>\n\n\n\n C\u00e2u C: 0<\/p>\n\n\n\n C\u00e2u D: 6<\/p>\n\n\n\n B\u00e0i t\u1eadp 4: L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<\/p>\n\n\n\n Cho \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn sau: x11 \u2013 x10 + x9 \u2013 x8. T\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn \u0111\u00e3 cho sau \u0111\u00f3 t\u00ednh t\u00edch t\u00ecm \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n C\u00e2u A: -1<\/p>\n\n\n\n C\u00e2u B: -2<\/p>\n\n\n\n C\u00e2u C: -3<\/p>\n\n\n\n C\u00e2u D: 0<\/p>\n\n\n\n B\u00e0i t\u1eadp 5: L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<\/p>\n\n\n\n Cho \u0111a th\u1ee9c sau: f(x) = x2 \u2013 10x + 9. \u0110\u00e2u l\u00e0 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho tr\u00ean.<\/p>\n\n\n\n C\u00e2u A: 1 v\u00e0 9<\/p>\n\n\n\n C\u00e2u B: -1 v\u00e0 -9<\/p>\n\n\n\n C\u00e2u C: -1 v\u00e0 9<\/p>\n\n\n\n C\u00e2u D: 1 v\u00e0 -9<\/p>\n\n\n\n D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp t\u1ef1 lu\u1eadn v\u1ec1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn th\u00f4ng d\u1ee5ng gi\u00fap c\u00e1c em \u00f4n luy\u1ec7n \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3.<\/p>\n\n\n\n C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp t\u1ef1 lu\u1eadn v\u1ec1 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c 1 bi\u1ebfn<\/p>\n\n\n\n B\u00e0i t\u1eadp 1: Cho \u0111a th\u1ee9c sau g(x) = x2 \u2013 x \u2013 6<\/p>\n\n\n\n T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a g(x) t\u1ea1i x = -1, -2, -3, 1, 2, 3<\/p>\n\n\n\n V\u1edbi nh\u1eefng gi\u00e1 tr\u1ecb \u0111\u00e3 cho tr\u00ean, gi\u00e1 tr\u1ecb x n\u00e0o l\u00e0 nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c \u0111\u00e3 cho g(x).<\/p>\n\n\n\n B\u00e0i t\u1eadp 2: Ch\u1ee9ng t\u1ecf \u0111a th\u1ee9c 10×2 + 3 kh\u00f4ng c\u00f3 nghi\u1ec7m.<\/p>\n\n\n\n B\u00e0i t\u1eadp 3: Cho \u0111a th\u1ee9c sau: x = x3 + 2×2 \u2013 3x + 1 ch\u1ee9ng minh r\u1eb1ng \u0111a th\u1ee9c \u0111\u00e3 cho ch\u1ec9 c\u00f3 duy nh\u1ea5t 1 nghi\u1ec7m nguy\u00ean<\/p>\n\n\n\n Nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn tr\u00ean l\u00e0 ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc l\u1edbp 7. Hy v\u1ecdng b\u00e0i gi\u1ea3ng v\u1ec1 l\u00fd thuy\u1ebft v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp tr\u00ean s\u1ebd gi\u00fap c\u00e1c em h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 \u00f4n t\u1eadp \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3. Trong su\u1ed1t qu\u00e1 tr\u00ecnh \u00f4n t\u1eadp, n\u1ebfu c\u00f3 b\u1ea5t k\u1ef3 th\u1eafc m\u1eafc ho\u1eb7c c\u00e2u h\u1ecfi li\u00ean quan \u0111\u1ebfn m\u00f4n h\u1ecdc, h\u00e3y li\u00ean h\u1ec7 v\u1edbi Vietlearn.org\/ \u0111\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p nhanh nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n <\/p><\/blockquote>\n\n\n\n \u0110a th\u1ee9c m\u1ed9t bi\u1ebfn \u2013 T\u00ecm hi\u1ec3u l\u00fd thuy\u1ebft v\u00e0 b\u00e0i t\u1eadp c\u00f9ng Vietlearn<\/p>\n\n\n\n C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 v\u00e0 c\u00e1ch<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn \u0110a th\u1ee9c m\u1ed9t bi\u1ebfn l\u00e0 m\u1ed9t trong nh\u1eefng ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 l\u00e0 d\u1ea1ng to\u00e1n \u0111i\u1ec3n h\u00ecnh trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n h\u1ecdc l\u1edbp 7. \u0110\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c d\u1ea1ng to\u00e1n n\u00e0y c\u1ea7n n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft c\u0169ng nh\u01b0 c\u00e1ch t\u00ecm nghi\u1ec7m c\u1ee7a \u0111a th\u1ee9c m\u1ed9t bi\u1ebfn. Ch\u00ednh v\u00ec […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-1031","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1031","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=1031"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1031\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}