{"id":28836,"date":"2021-03-30T13:00:35","date_gmt":"2021-03-30T13:00:35","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28836"},"modified":"2024-09-22T02:04:54","modified_gmt":"2024-09-22T02:04:54","slug":"%e4%ba%8c%e6%ac%a1%e5%a4%9a%e9%a1%b9%e5%bc%8f%e5%92%8c2n%e6%ac%a1%e5%a4%9a%e9%a1%b9%e5%bc%8f%e7%9a%84%e5%9b%a0%e5%bc%8f%e5%88%86%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e4%ba%8c%e6%ac%a1%e5%a4%9a%e9%a1%b9%e5%bc%8f%e5%92%8c2n%e6%ac%a1%e5%a4%9a%e9%a1%b9%e5%bc%8f%e7%9a%84%e5%9b%a0%e5%bc%8f%e5%88%86%e8%a7%a3\/","title":{"rendered":"\u4e8c\u6b21\u591a\u9879\u5f0f\u548c2n\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3"},"content":{"rendered":"<p><center><\/p>\n<h1>\u4e8c\u6b21\u591a\u9879\u5f0f\u548c2n\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n   \u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u56de\u987e\u4e8c\u6b21\u591a\u9879\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span> \u548c 2n \u6b21\u591a\u9879\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">(2n)<\/span>-\u591a\u9879\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span> \u7684\u56e0\u5f0f\u5206\u89e3\u8fc7\u7a0b\uff0c\u5c06\u5b83\u4eec\u5206\u89e3\u4e3a\u7b80\u5355\u56e0\u5f0f\u3002\u6211\u4eec\u5c06\u6570\u5b66\u5730\u63a8\u5bfc\u8fd9\u4e9b\u8fc7\u7a0b\uff0c\u5e76\u5c55\u793a\u5b9e\u9645\u4f8b\u5b50\u3002<\/em><\/p>\n<p>   <strong>\u5b66\u4e60\u76ee\u6807<\/strong><\/p>\n<ol style=\"text-align: left;\">\n<li><strong>\u5b66\u4e60<\/strong>\u5982\u4f55\u5bf9\u5f62\u5982 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span> \u7684\u4e8c\u6b21\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<\/li>\n<li><strong>\u63a8\u5bfc<\/strong>\u5e76\u4f7f\u7528\u4e8c\u6b21\u516c\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">x = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}<\/span> \u6765\u627e\u5230\u6839\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u56e0\u5f0f\u5206\u89e3\u6280\u672f\u5230\u5f62\u5982 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span> \u7684 2n \u6b21\u591a\u9879\u5f0f\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u4e8c\u6b21\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u6240\u9700\u7684\u6761\u4ef6\u3002<\/li>\n<li><strong>\u4f7f\u7528<\/strong>\u5b8c\u5168\u5e73\u65b9\u7684\u65b9\u6cd5\u6765\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<\/li>\n<\/ol>\n<p>   <strong>\u76ee\u5f55\uff1a<\/strong><br \/>\n   <a href=\"#1\">\u7b80\u4ecb<\/a><br \/>\n   <a href=\"#2\">\u4e8c\u6b21\u591a\u9879\u5f0f\u548c2n\u6b21\u591a\u9879\u5f0f<\/a><br \/>\n   <a href=\"#3\">\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3<\/a><br \/>\n   <a href=\"#4\">\u4e8c\u6b21\u56db\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u6269\u5c55<\/a><br \/>\n   <a href=\"#5\">\u4f8b\u9898<\/a>\n   <\/p>\n<p><\/center><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ddTfUR7QBfY\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u7b80\u4ecb<\/h2>\n<p style=\"text-align: justify;\">\u5b66\u4e60\u5982\u4f55\u5bf9\u4e8c\u6b21\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u662f\u5f00\u59cb\u5b66\u4e60\u8bb8\u591a\u5176\u4ed6\u56e0\u5f0f\u5206\u89e3\u6280\u672f\u7684\u7b2c\u4e00\u6b65\u3002\u6b63\u56e0\u4e3a\u5982\u6b64\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u63a2\u8ba8\u8fd9\u4e00\u6280\u672f\uff0c\u5e76\u5c3d\u53ef\u80fd\u6269\u5c55\u5b83\u7684\u5e94\u7528\u3002\u5728\u7ed3\u675f\u65f6\uff0c\u60a8\u5c06\u4e0d\u4ec5\u5b66\u4f1a\u5bf9\u4e8c\u6b21\u591a\u9879\u5f0f\uff082\u6b21\u65b9\u7a0b\uff09\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd8\u5c06\u4f7f\u7528\u8fd9\u4e9b\u6280\u672f\u6765\u5206\u89e3\u4efb\u610f\u7684 2n \u6b21\u591a\u9879\u5f0f\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u4e8c\u6b21\u591a\u9879\u5f0f\u548c2n\u6b21\u591a\u9879\u5f0f<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=96s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e8c\u6b21\u591a\u9879\u5f0f\u662f\u4e8c\u6b21\u65b9\u7a0b\u3002<\/strong><\/a> \u4ece\u8fd9\u4e00\u70b9\u51fa\u53d1\uff0c\u4e8c\u6b21\u591a\u9879\u5f0f\u662f\u4efb\u4f55\u5f62\u5982<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2}+bx +c <\/span>\n<p style=\"text-align: justify;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u4e14 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>\u3002\u7136\u800c\uff0c\u6211\u4eec\u7684\u7814\u7a76\u4e0d\u4ec5\u4ec5\u96c6\u4e2d\u5728\u56e0\u5f0f\u5206\u89e3\u8fd9\u79cd\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\u4e0a\uff0c\u6211\u4eec\u8fd8\u4f1a\u8ba8\u8bba\u5176\u4e2d\u7684\u5e7f\u4e49\u5f62\u5f0f\uff0c\u5176\u4e2d\u4e8c\u6b21\u591a\u9879\u5f0f\u53ea\u662f\u4e00\u4e2a\u7279\u6b8a\u7684\u4f8b\u5b50\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a 2n \u6b21\u591a\u9879\u5f0f\u3002\u8fd9\u4e00\u5e7f\u4e49\u5f62\u5f0f\u6db5\u76d6\u4e86\u6240\u6709\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n}+bx^n +c <\/span>\n<p style=\"text-align: justify;\">\u9664\u6b64\u4e4b\u5916\uff0c\u5047\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u4e14 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>\uff0c\u53d6\u4efb\u610f <span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{N}<\/span>\u3002\u6b64\u7c7b\u591a\u9879\u5f0f\u7684\u793a\u4f8b\u5305\u62ec\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3x^2 -x + 1<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 7x^4 +5x^2 + 3<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = -4x^6 +12x^3 + 2<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = 21x^8 -75 x^4 -9<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u7b49\u7b49\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=193s\" target=\"_blank\" rel=\"noopener\"><strong>\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u901a\u5f0f\u4e3a<\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2}+bx +c \\;\\; , \\;\\; a\\neq 0 <\/span>\n<p style=\"text-align: justify;\">\u56e0\u5f0f\u5206\u89e3\u662f\u5c06\u590d\u6742\u591a\u9879\u5f0f\u5206\u89e3\u4e3a\u4e24\u4e2a\u66f4\u7b80\u5355\u591a\u9879\u5f0f\u4e58\u79ef\u7684\u8fc7\u7a0b\u3002\u56e0\u6b64\uff0c\u5982\u679c\u53ef\u4ee5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u5219\u5b58\u5728\u5e38\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta,\\gamma,\\delta \\in\\mathbb{R}<\/span>\uff0c\u4e14 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\gamma \\neq 0<\/span>\uff0c\u4f7f\u5f97\uff1a<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\">= (\\alpha x + \\beta)(\\gamma x + \\delta) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\">= \\alpha \\gamma \\left(x +\\displaystyle \\frac{\\beta}{\\alpha}\\right)\\left(x + \\frac{\\delta}{\\gamma}\\right) <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u7531\u4e8e\u5de6\u53f3\u4e24\u8fb9\u76f8\u7b49\uff0c\u56e0\u6b64\u5f53\u4e00\u8fb9\u4e3a\u96f6\u65f6\uff0c\u53e6\u4e00\u8fb9\u4e5f\u5fc5\u987b\u4e3a\u96f6\u3002\u7ed3\u679c\u662f\u53f3\u8fb9\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\beta\/\\alpha<\/span> \u6216 <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\delta\/\\gamma<\/span> \u65f6\u4e3a\u96f6\u3002\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5de6\u8fb9\u5728\u4ec0\u4e48\u60c5\u51b5\u4e0b\u4e3a\u96f6\u3002\u6211\u4eec\u5c06\u5f97\u5230<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + c<\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = 0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = -c<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + \\displaystyle \\frac{b}{a}x <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = - \\displaystyle \\frac{c}{a}<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right; background-color: #ffc0c0;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + \\displaystyle \\frac{b}{a}x + \\frac{b^2}{4a^2}<\/span><\/td>\n<td style=\"text-align: left; background-color: #ffc0c0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> =\\displaystyle \\frac{b^2}{4a^2} -\\frac{c}{a} = \\frac{ab^2 - 4a^2 c}{4a^3} = \\frac{b^2 - 4ac }{4a^2}<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(x + \\displaystyle \\frac{b}{2a}\\right)^2<\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\displaystyle \\frac{b^2 - 4ac }{4a^2} <\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right;\"><span class=\"katex-eq\" data-katex-display=\"false\"> x + \\displaystyle \\frac{b}{2a} <\/span><\/td>\n<td style=\"text-align: left;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\pm \\sqrt{\\displaystyle \\frac{b^2 - 4ac }{4a^2}} = \\frac{\\pm\\sqrt{b^2 - 4ac }}{2a} <\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right; background-color: #a0ffa0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> x <\/span><\/td>\n<td style=\"text-align: left; background-color: #a0ffa0;\"><span class=\"katex-eq\" data-katex-display=\"false\"> = \\displaystyle \\frac{-b \\pm\\sqrt{b^2 - 4ac }}{2a} <\/span> \u2705<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u6839\u636e\u8fd9\u4e00\u63a8\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u56e0\u5f0f\u5206\u89e3\u7684\u5e0c\u814a\u5b57\u6bcd\u5e38\u6570\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff08\u4e00\u822c\u60c5\u51b5\u4e0b\uff09\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\gamma = a<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\beta}{\\alpha} = - \\left(\\frac{-b + \\sqrt{b^2 - 4ac }}{2a} \\right)<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\delta}{\\gamma} = - \\left(\\frac{-b - \\sqrt{b^2 - 4ac }}{2a} \\right)<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u7531\u6b64\u6211\u4eec\u5f97\u51fa\u4e00\u9879\u6280\u672f\uff0c\u53ef\u4ee5\u5206\u89e3\u4efb\u4f55\u4e8c\u6b21\u591a\u9879\u5f0f\u3002\u5982\u679c\u4e0d\u80fd\u5206\u89e3\uff0c\u5219\u901a\u8fc7\u6839\u53f7\u5185\u7684\u6570\u544a\u8bc9\u4f60\u7b54\u6848\uff1a\u5982\u679c\u8be5\u6570\u4e3a\u8d1f\uff0c\u5219\u65e0\u6cd5\u5206\u89e3\uff08\u4f7f\u7528\u5b9e\u6570\uff09\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5f15\u5165\u7b26\u53f7\u7ea6\u5b9a\u7b80\u5316\u8fd9\u4e00\u8fc7\u7a0b\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">x_1 =\\displaystyle \\frac{-b + \\sqrt{b^2 - 4ac }}{2a} <\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">x_2 =\\displaystyle \\frac{-b - \\sqrt{b^2 - 4ac }}{2a} <\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u603b\u800c\u8a00\u4e4b\uff0c\u56e0\u5f0f\u5206\u89e3\u53ef\u4ee5\u7b80\u5316\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{x_{1,2} = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}}<\/span> \u2705<\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u6700\u7ec8\u7684\u56e0\u5f0f\u5206\u89e3\u5f62\u5f0f\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{P(x) = ax^2 +bx + c = a(x-x_1)(x - x_2)}<\/span>\u2705<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u4e8c\u6b21\u56db\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u6269\u5c55<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=997s\" target=\"_blank\" rel=\"noopener\"><strong>\u8be5\u6280\u672f\u8fd8\u53ef\u4ee5\u7528\u4e8e\u5206\u89e3\u4e8c\u6b21\u56db\u6b21\u591a\u9879\u5f0f<\/strong><\/a>\uff0c\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = ax^4 + bx^2 + c = a(x^2)^2 + bx^2 + c =a (x^2 - x_1^2)(x^2-x_2^2) <\/span>\n<p style=\"text-align: justify;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\"> x^2_{1,2} = \\displaystyle \\dfrac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}<\/span>\u3002\u56e0\u6b64\uff0c\u4f60\u53ef\u4ee5\u5199\u4f5c\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = ax^4 + bx^2 + c = a\\left(x^2 - \\displaystyle \\dfrac{-b + \\sqrt{b^2 - 4ac }}{2a}\\right) \\left(x^2- \\dfrac{-b - \\sqrt{b^2 - 4ac }}{2a}\\right) <\/span>\n<p style=\"text-align: justify;\">\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u4f60\u9700\u8981\u5c0f\u5fc3\uff0c\u56e0\u4e3a\u63a5\u4e0b\u6765\u7684\u6b65\u9aa4\u6709\u5176\u9650\u5236\u3002\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">x_1^2<\/span> \u4e0d\u662f\u6b63\u6570\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7\u548c\u5dee\u516c\u5f0f\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">(x^2 - x_1^2) = (x-x_1)(x + x_1)<\/span> \u8fdb\u884c\u5206\u89e3\uff1b\u5426\u5219\uff0c\u4f60\u5c06\u9047\u5230\u590d\u6570\uff0c\u56e0\u6b64\u65e0\u6cd5\u5728\u5b9e\u6570\u8303\u56f4\u5185\u7ee7\u7eed\u5206\u89e3\u3002\u5982\u679c\u6240\u6709\u6839\u90fd\u5f88\u597d\u5730\u5b9a\u4e49\uff0c\u4f60\u53ef\u4ee5\u5199\u4f5c\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nQ(x) &amp;= ax^4 + bx^2 + c \\\\ \\\\\n\n     &amp; = a \\left(x -\\displaystyle \\sqrt{\\frac{-b + \\sqrt{b^2 - 4ac }}{2a}}\\right) \\left(x + \\displaystyle \\sqrt{\\frac{-b + \\sqrt{b^2 - 4ac }}{2a}}\\right) \\\\ \\\\\n\n&amp; \\left(x- \\displaystyle \\sqrt{\\frac{-b - \\sqrt{b^2 - 4ac }}{2a}}\\right) \\left(x+ \\sqrt{\\displaystyle \\frac{-b - \\sqrt{b^2 - 4ac }}{2a}}\\right)\n\n\\end{array}<\/span>\n<p style=\"text-align: justify;\">\u5426\u5219\uff0c\u4f60\u5c06\u505c\u5728\u524d\u4e00\u6b65\u3002<\/p>\n<h3>2n\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u6269\u5c55<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=1521s\" target=\"_blank\" rel=\"noopener\"><strong>\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u7406\u89e3\u5b83\u6307\u5411\u4f55\u5904\uff0c\u5bf9\u4e8e 2n \u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3<\/strong><\/a>\uff0c\u53ea\u9700\u91cd\u65b0\u8868\u8fbe\u5b83\u5e76\u5728\u6839\u660e\u786e\u65f6\u5e94\u7528\u4e0a\u8ff0\u65b9\u6cd5\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = a(x^n)^{2}+b (x^n) +c = a(x^n-x_1^n)(x^n-x_2^n) <\/span>\n<p style=\"text-align: justify;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">x^n_{1,2} =\\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}<\/span>\u3002\u7136\u540e\uff0c\u5728\u6ca1\u6709\u590d\u6570\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u4f7f\u7528\u548c\u5dee\u516c\u5f0f\u8fdb\u884c\u5206\u89e3\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u4f8b\u9898<\/h2>\n<p style=\"text-align: justify;\">\u73b0\u5728\u8f6e\u5230\u4f60\u8fd0\u7528\u8fd9\u4e9b\u6280\u672f\u89e3\u51b3\u4e00\u4e9b\u7ec3\u4e60\u3002\u8fd9\u4e9b\u968f\u673a\u9009\u62e9\u7684\u591a\u9879\u5f0f\u5c06\u5e2e\u52a9\u4f60\u8bc6\u522b\u56e0\u5f0f\u5206\u89e3\u65f6\u53ef\u80fd\u9047\u5230\u7684\u96be\u70b9\u3002<\/p>\n<h3>\u7b2c\u4e00\u8f6e<\/h3>\n<p style=\"text-align: justify;\">\u8fd9\u4e9b\u591a\u9879\u5f0f\u662f\u672c\u6587\u5f00\u5934\u7684\u793a\u4f8b<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3x^2 -x + 1<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 7x^4 +5x^2 + 3<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = -4x^6 +12x^3 + 2<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = 21x^8 -75 x^4 -9<\/span><\/li>\n<\/ol>\n<h3>\u7b2c\u4e8c\u8f6e<\/h3>\n<p style=\"text-align: justify;\">\u8fd9\u4e9b\u591a\u9879\u5f0f\u7a0d\u5fae\u56f0\u96be\u4e00\u4e9b\u3002<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 78x^2 -21x - 13<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 27x^4 +5x^2 - 14<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">R(x) = 9x^6 +12x^3 - 16<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(x) = -9x^8 -2 x^4 + 10<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">T(x) = 5x^{12} -2 x^6 - 15<\/span><\/li>\n<\/ol>\n<h3>\u7ec3\u4e60\u89e3\u7b54<\/h3>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ilNTFyF7Hmo\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u6b21\u591a\u9879\u5f0f\u548c2n\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3 \u6458\u8981\uff1a \u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u56de\u987e\u4e8c\u6b21\u591a\u9879\u5f0f \u548c 2n \u6b21\u591a\u9879\u5f0f -\u591a\u9879\u5f0f \u7684\u56e0\u5f0f\u5206\u89e3\u8fc7\u7a0b\uff0c\u5c06\u5b83\u4eec\u5206\u89e3\u4e3a\u7b80\u5355\u56e0\u5f0f\u3002\u6211\u4eec\u5c06\u6570\u5b66\u5730\u63a8\u5bfc\u8fd9\u4e9b\u8fc7\u7a0b\uff0c\u5e76\u5c55\u793a\u5b9e\u9645\u4f8b\u5b50\u3002 \u5b66\u4e60\u76ee\u6807 \u5b66\u4e60\u5982\u4f55\u5bf9\u5f62\u5982 \u7684\u4e8c\u6b21\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 \u63a8\u5bfc\u5e76\u4f7f\u7528\u4e8c\u6b21\u516c\u5f0f \u6765\u627e\u5230\u6839\u3002 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\u3002\u7136\u800c\uff0c\u6211\u4eec\u7684\u7814\u7a76\u4e0d\u4ec5\u4ec5\u96c6\u4e2d\u5728\u56e0\u5f0f\u5206\u89e3\u8fd9\u79cd\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\u4e0a\uff0c\u6211\u4eec\u8fd8\u4f1a\u8ba8\u8bba\u5176\u4e2d\u7684\u5e7f\u4e49\u5f62\u5f0f\uff0c\u5176\u4e2d\u4e8c\u6b21\u591a\u9879\u5f0f\u53ea\u662f\u4e00\u4e2a\u7279\u6b8a\u7684\u4f8b\u5b50\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a 2n \u6b21\u591a\u9879\u5f0f\u3002\u8fd9\u4e00\u5e7f\u4e49\u5f62\u5f0f\u6db5\u76d6\u4e86\u6240\u6709\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\uff1a \u9664\u6b64\u4e4b\u5916\uff0c\u5047\u8bbe \u4e14 \uff0c\u53d6\u4efb\u610f \u3002\u6b64\u7c7b\u591a\u9879\u5f0f\u7684\u793a\u4f8b\u5305\u62ec\uff1a \u7b49\u7b49\u3002 \u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3 \u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u901a\u5f0f\u4e3a 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