{"id":33679,"date":"2021-03-30T13:00:39","date_gmt":"2021-03-30T13:00:39","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33679"},"modified":"2025-07-30T18:53:22","modified_gmt":"2025-07-30T18:53:22","slug":"%e4%ba%8c%e6%ac%a1%e3%81%8a%e3%82%88%e3%81%b32n-%e4%ba%8c%e6%ac%a1%e5%a4%9a%e9%a0%85%e5%bc%8f%e3%81%ae%e5%9b%a0%e6%95%b0%e5%88%86%e8%a7%a3","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e4%ba%8c%e6%ac%a1%e3%81%8a%e3%82%88%e3%81%b32n-%e4%ba%8c%e6%ac%a1%e5%a4%9a%e9%a0%85%e5%bc%8f%e3%81%ae%e5%9b%a0%e6%95%b0%e5%88%86%e8%a7%a3\/","title":{"rendered":"\u4e8c\u6b21\u304a\u3088\u3073(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3"},"content":{"rendered":"<p><center><\/p>\n<h1>\u4e8c\u6b21\u304a\u3088\u3073(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3<\/h1>\n<p><em><strong>\u8981\u7d04\uff1a<\/strong><br \/>\n   \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u4e8c\u6b21\u591a\u9805\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span> \u304a\u3088\u3073 (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span> \u306e\u56e0\u6570\u5206\u89e3\u30d7\u30ed\u30bb\u30b9\u3092\u8a73\u7d30\u306b\u691c\u8a0e\u3057\u3001\u305d\u308c\u3089\u3092\u5358\u7d14\u306a\u56e0\u6570\u3078\u3068\u5206\u89e3\u3059\u308b\u624b\u9806\u3092\u5b66\u3073\u307e\u3059\u3002\u6570\u5b66\u7684\u306b\u624b\u9806\u3092\u5c55\u958b\u3057\u3001\u5b9f\u7528\u7684\u306a\u4f8b\u3082\u63d0\u793a\u3057\u307e\u3059\u3002<\/em><\/p>\n<p>   <strong>\u5b66\u7fd2\u76ee\u6a19<\/strong><\/p>\n<ol style=\"text-align: left;\">\n<li><strong>\u5b66\u3076\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^2 + bx + c<\/span> \u306e\u5f62\u3092\u3057\u305f\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3\u65b9\u6cd5\u3092\u7fd2\u5f97\u3059\u308b\u3002<\/li>\n<li><strong>\u5c0e\u51fa\u3059\u308b\uff1a<\/strong> \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u516c\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">x = \\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}<\/span> \u3092\u5c0e\u51fa\u3057\u3001\u305d\u308c\u3092\u7528\u3044\u3066\u6839\u3092\u6c42\u3081\u308b\u3002<\/li>\n<li><strong>\u9069\u7528\u3059\u308b\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = ax^{2n} + bx^n + c<\/span> \u306e\u5f62\u3092\u3057\u305f (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u306b\u56e0\u6570\u5206\u89e3\u306e\u6280\u8853\u3092\u5fdc\u7528\u3059\u308b\u3002<\/li>\n<li><strong>\u8a8d\u8b58\u3059\u308b\uff1a<\/strong> \u4e8c\u6b21\u578b\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6761\u4ef6\u3092\u7406\u89e3\u3059\u308b\u3002<\/li>\n<li><strong>\u4f7f\u7528\u3059\u308b\uff1a<\/strong> \u56e0\u6570\u5206\u89e3\u306e\u904e\u7a0b\u306b\u304a\u3044\u3066\u5e73\u65b9\u5b8c\u6210\u6cd5\u3092\u5229\u7528\u3059\u308b\u3002<\/li>\n<\/ol>\n<p>   <strong>\u76ee\u6b21\uff1a<\/strong><br \/>\n   <a href=\"#1\">\u306f\u3058\u3081\u306b<\/a><br \/>\n   <a href=\"#2\">\u4e8c\u6b21\u591a\u9805\u5f0f\u3068 (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f<\/a><br \/>\n   <a href=\"#3\">\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3<\/a><br \/>\n   <a href=\"#4\">(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u3078\u306e\u5c55\u958b<\/a><br \/>\n   <a href=\"#5\">\u4f8b\u984c\u6f14\u7fd2<\/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>\u306f\u3058\u3081\u306b<\/h2>\n<p style=\"text-align: justify;\">\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3\u3092\u7fd2\u5f97\u3059\u308b\u3053\u3068\u306f\u3001\u4ed6\u306e\u591a\u304f\u306e\u56e0\u6570\u5206\u89e3\u6280\u8853\u3092\u5b66\u3076\u4e0a\u3067\u306e\u51fa\u767a\u70b9\u3068\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u6280\u8853\u3092\u6df1\u304f\u6398\u308a\u4e0b\u3052\u3001\u305d\u306e\u5fdc\u7528\u7bc4\u56f2\u3092\u53ef\u80fd\u306a\u9650\u308a\u5e83\u3052\u3066\u3044\u304d\u307e\u3059\u3002\u8b1b\u7fa9\u306e\u7d42\u308f\u308a\u306b\u306f\u30012\u6b21\uff08\u6b21\u65702\uff09\u306e\u591a\u9805\u5f0f\u3060\u3051\u3067\u306a\u304f\u3001(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u3082\u540c\u69d8\u306e\u624b\u6cd5\u3067\u56e0\u6570\u5206\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u4e8c\u6b21\u591a\u9805\u5f0f\u304a\u3088\u3073(2n)-\u4e8c\u6b21\u591a\u9805\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\u9805\u5f0f\u3068\u306f\u6b21\u6570\u304c2\u306e\u591a\u9805\u5f0f\u3067\u3059\u3002<\/strong><\/a> \u3053\u306e\u5b9a\u7fa9\u306b\u3088\u308a\u3001\u4e8c\u6b21\u591a\u9805\u5f0f\u3068\u306f\u6b21\u306e\u5f62\u3092\u6301\u3064\u4efb\u610f\u306e\u95a2\u6570\u3092\u6307\u3057\u307e\u3059\u3002<\/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;\">\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u304b\u3064 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span> \u3068\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u6211\u3005\u306e\u7814\u7a76\u306e\u7126\u70b9\u306f\u3053\u306e\u5f62\u306e\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3\u306b\u9650\u5b9a\u3055\u308c\u308b\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3080\u3057\u308d\u3001\u4e8c\u6b21\u591a\u9805\u5f0f\u3092\u7279\u6b8a\u306a\u5834\u5408\u3068\u307f\u306a\u3057\u305f\u4e00\u822c\u5316\u3055\u308c\u305f\u5f62\u3092\u6271\u3044\u307e\u3059\u3002\u3053\u308c\u304c (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u306e\u4e00\u822c\u5316\u306b\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u3059\u3079\u3066\u306e\u591a\u9805\u5f0f\u3092\u542b\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\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;\">\u3053\u3053\u3067\u3082 <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u304b\u3064 <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span> \u306b\u52a0\u3048\u3066\u3001\u4efb\u610f\u306e\u81ea\u7136\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{N}<\/span> \u3092\u3068\u308a\u307e\u3059\u3002\u3053\u306e\u7a2e\u306e\u591a\u9805\u5f0f\u306e\u4f8b\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\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;\">\u3053\u306e\u3088\u3046\u306b\u3001\u4e00\u822c\u7684\u306a\u5f62\u3067\u8a18\u8ff0\u3055\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\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>\u3059\u3067\u306b\u78ba\u8a8d\u3057\u305f\u3088\u3046\u306b\u3001\u6b21\u65702\u306e\u591a\u9805\u5f0f\u306f\u6b21\u306e\u4e00\u822c\u5f62\u3092\u6301\u3061\u307e\u3059\uff1a<\/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\u6570\u5206\u89e3\u3068\u306f\u3001\u8907\u96d1\u306a\u591a\u9805\u5f0f\u3092\u3088\u308a\u5358\u7d14\u306a2\u3064\u306e\u591a\u9805\u5f0f\u306e\u7a4d\u306b\u5206\u89e3\u3059\u308b\u904e\u7a0b\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u56e0\u6570\u5206\u89e3\u304c\u53ef\u80fd\u306a\u5834\u5408\u3001\u5b9f\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta,\\gamma,\\delta \\in\\mathbb{R}<\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\gamma \\neq 0<\/span>\uff09\u304c\u5b58\u5728\u3057\u3066\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\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;\">\u5de6\u8fba\u3068\u53f3\u8fba\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u7247\u65b9\u304c0\u306b\u306a\u308b\u3068\u4ed6\u65b9\u3082\u5fc5\u305a0\u306b\u306a\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u53f3\u8fba\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\beta\/\\alpha<\/span> \u307e\u305f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x=-\\delta\/\\gamma<\/span> \u306e\u3068\u304d\u306b0\u306b\u306a\u308a\u307e\u3059\u3002\u3067\u306f\u3001\u5de6\u8fba\u304c0\u306b\u306a\u308b\u306e\u306f\u3069\u306e\u3088\u3046\u306a\u5024\u306e\u3068\u304d\u3067\u3057\u3087\u3046\u304b\u3002\u6b21\u306b\u305d\u308c\u3092\u691c\u8a0e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/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;\">\u3053\u306e\u63a8\u8ad6\u306b\u57fa\u3065\u304d\u3001\u56e0\u6570\u5206\u89e3\u306b\u7528\u3044\u308b\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u306e\u5b9a\u6570\u306f\u3001\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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;\">\u3053\u308c\u306b\u3088\u308a\u3001\u4efb\u610f\u306e2\u6b21\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u305f\u3081\u306e\u6280\u8853\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3082\u3057\u56e0\u6570\u5206\u89e3\u304c\u4e0d\u53ef\u80fd\u3067\u3042\u308c\u3070\u3001\u305d\u308c\u306f\u5e73\u65b9\u6839\u306e\u4e2d\u306e\u6570\u5024\uff08\u5224\u5225\u5f0f\uff09\u306b\u3088\u3063\u3066\u793a\u3055\u308c\u307e\u3059\u3002\u305d\u306e\u5024\u304c\u8ca0\u306e\u5834\u5408\u3001\u5b9f\u6570\u306e\u7bc4\u56f2\u3067\u306f\u56e0\u6570\u5206\u89e3\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u306e\u8b70\u8ad6\u3092\u7c21\u6f54\u306b\u3059\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8a18\u6cd5\u3092\u5c0e\u5165\u3057\u307e\u3059\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;\">\u3053\u308c\u3089\u306f\u4ee5\u4e0b\u306e\u3088\u304f\u77e5\u3089\u308c\u305f\u516c\u5f0f\u306b\u307e\u3068\u3081\u3089\u308c\u307e\u3059\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;\">\u3057\u305f\u304c\u3063\u3066\u3001\u56e0\u6570\u5206\u89e3\u306e\u7d50\u679c\u306f\u6700\u7d42\u7684\u306b\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\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>\u56db\u6b21\uff08\u4e8c\u91cd\uff09\u591a\u9805\u5f0f\u3078\u306e\u56e0\u6570\u5206\u89e3\u306e\u62e1\u5f35<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=997s\" target=\"_blank\" rel=\"noopener\"><strong>\u3053\u306e\u624b\u6cd5\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u56db\u6b21\uff08\u4e8c\u91cd\uff09\u591a\u9805\u5f0f\u306b\u3082\u5fdc\u7528\u3067\u304d\u307e\u3059\uff1a<\/strong><\/a><\/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;\">\u3053\u3053\u3067\u3001<span class=\"katex-eq\" data-katex-display=\"false\"> x^2_{1,2} = \\displaystyle \\dfrac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}<\/span> \u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\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;\">\u3053\u3053\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u306f\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002<span class=\"katex-eq\" data-katex-display=\"false\">x_1^2<\/span> \u304c\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u9650\u308a\u3001\u5dee\u7a4d\u516c\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">(x^2 - x_1^2) = (x - x_1)(x + x_1)<\/span> \u3092\u9069\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f\u8907\u7d20\u6570\u304c\u73fe\u308c\u3001\u5b9f\u6570\u306e\u7bc4\u56f2\u3067\u56e0\u6570\u5206\u89e3\u3092\u7d9a\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3059\u3079\u3066\u306e\u6839\u304c\u5b9a\u7fa9\u3067\u304d\u308b\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u56e0\u6570\u5206\u89e3\u3067\u304d\u307e\u3059\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;\">\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f\u3001\u524d\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u56e0\u6570\u5206\u89e3\u3092\u6b62\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u3078\u306e\u56e0\u6570\u5206\u89e3\u306e\u4e00\u822c\u5316<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ddTfUR7QBfY&amp;t=1521s\" target=\"_blank\" rel=\"noopener\"><strong>\u3053\u306e\u6d41\u308c\u306b\u3088\u308a\u3001(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u65b9\u6cd5\u306e\u65b9\u5411\u6027\u304c\u7406\u89e3\u3067\u304d\u305f\u3068\u601d\u3044\u307e\u3059\u3002<\/strong><\/a> \u3042\u3068\u306f\u8868\u8a18\u306e\u4ed5\u65b9\u3092\u518d\u69cb\u6210\u3057\u3001\u5148\u307b\u3069\u306e\u624b\u6cd5\u3092\u6839\u304c\u5b9a\u7fa9\u3067\u304d\u308b\u7bc4\u56f2\u3067\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\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;\">\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">x^n_{1,2} =\\displaystyle \\frac{-b \\pm \\sqrt{b^2 - 4ac }}{2a}<\/span> \u3068\u3057\u3001\u8907\u7d20\u6570\u304c\u51fa\u73fe\u3057\u306a\u3044\u5834\u5408\u306b\u306f\u5dee\u7a4d\u516c\u5f0f\u3092\u7528\u3044\u3066\u3055\u3089\u306b\u5206\u89e3\u3057\u307e\u3059\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u4f8b\u984c\u6f14\u7fd2\uff1a<\/h2>\n<p style=\"text-align: justify;\">\u3053\u3053\u304b\u3089\u306f\u3001\u3042\u306a\u305f\u81ea\u8eab\u304c\u3053\u308c\u3089\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u6f14\u7fd2\u306b\u53d6\u308a\u7d44\u3080\u756a\u3067\u3059\u3002\u4ee5\u4e0b\u306b\u793a\u3059\u591a\u9805\u5f0f\u306f\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3070\u308c\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u56e0\u6570\u5206\u89e3\u306e\u969b\u306b\u906d\u9047\u3059\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u3055\u307e\u3056\u307e\u306a\u56f0\u96e3\u3092\u628a\u63e1\u3059\u308b\u306e\u306b\u975e\u5e38\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>\u7b2c1\u30e9\u30a6\u30f3\u30c9<\/h3>\n<p style=\"text-align: justify;\">\u3053\u308c\u3089\u306e\u591a\u9805\u5f0f\u306f\u3001\u3053\u306e\u8b1b\u7fa9\u306e\u5192\u982d\u3067\u4f8b\u3068\u3057\u3066\u6319\u3052\u305f\u3082\u306e\u3067\u3059\u3002<\/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>\u7b2c2\u30e9\u30a6\u30f3\u30c9<\/h3>\n<p style=\"text-align: justify;\">\u3053\u3061\u3089\u306f\u3084\u3084\u96e3\u6613\u5ea6\u306e\u9ad8\u3044\u6f14\u7fd2\u554f\u984c\u3067\u3059\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>\u6f14\u7fd2\u554f\u984c\u306e\u89e3\u8aac\u52d5\u753b<\/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\u304a\u3088\u3073(2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3 \u8981\u7d04\uff1a \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u4e8c\u6b21\u591a\u9805\u5f0f \u304a\u3088\u3073 (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f \u306e\u56e0\u6570\u5206\u89e3\u30d7\u30ed\u30bb\u30b9\u3092\u8a73\u7d30\u306b\u691c\u8a0e\u3057\u3001\u305d\u308c\u3089\u3092\u5358\u7d14\u306a\u56e0\u6570\u3078\u3068\u5206\u89e3\u3059\u308b\u624b\u9806\u3092\u5b66\u3073\u307e\u3059\u3002\u6570\u5b66\u7684\u306b\u624b\u9806\u3092\u5c55\u958b\u3057\u3001\u5b9f\u7528\u7684\u306a\u4f8b\u3082\u63d0\u793a\u3057\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19 \u5b66\u3076\uff1a \u306e\u5f62\u3092\u3057\u305f\u4e8c\u6b21\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3\u65b9\u6cd5\u3092\u7fd2\u5f97\u3059\u308b\u3002 \u5c0e\u51fa\u3059\u308b\uff1a \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u516c\u5f0f \u3092\u5c0e\u51fa\u3057\u3001\u305d\u308c\u3092\u7528\u3044\u3066\u6839\u3092\u6c42\u3081\u308b\u3002 \u9069\u7528\u3059\u308b\uff1a \u306e\u5f62\u3092\u3057\u305f (2n)-\u4e8c\u6b21\u591a\u9805\u5f0f\u306b\u56e0\u6570\u5206\u89e3\u306e\u6280\u8853\u3092\u5fdc\u7528\u3059\u308b\u3002 \u8a8d\u8b58\u3059\u308b\uff1a 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