{"id":11118,"date":"2022-11-19T22:06:27","date_gmt":"2022-11-19T13:06:27","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11118"},"modified":"2022-11-25T15:55:25","modified_gmt":"2022-11-25T06:55:25","slug":"higher-degree-polynomials","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/higher-degree-polynomials.html","title":{"rendered":"\u9ad8\u6b21\u65b9\u7a0b\u5f0f\uff1a\u56e0\u6570\u5206\u89e3\u3001\u56e0\u6570\u5b9a\u7406\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2"},"content":{"rendered":"\n<p>\u79c1\u305f\u3061\u304c\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u591a\u304f\u306f\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3084\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3084\u56db\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f3\u3064\u306e\u89e3\u304c\u3042\u308a\u3001\u56db\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f4\u3064\u306e\u89e3\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e09\u6b21\u4ee5\u4e0a\u306e\u65b9\u7a0b\u5f0f\u3092\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3068\u3044\u3044\u307e\u3059\u3002\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u304d\u3001\u516c\u5f0f\u306e\u5229\u7528\u3084\u56e0\u6570\u5b9a\u7406\u306e\u6d3b\u7528\u306a\u3069\u3001\u89e3\u304d\u65b9\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u6b21\u6570\u3092\u4e0b\u3052\u305f\u308a\u3001\u4e8c\u91cd\u89e3\u3092\u3082\u3064\u5834\u5408\u306e\u8a08\u7b97\u3092\u3057\u305f\u308a\u3068\u72ec\u81ea\u306e\u554f\u984c\u304c\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3067\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3082\u5b66\u3070\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u554f\u984c\u306e\u89e3\u304d\u65b9\u304c\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u306f\u4e3b\u306b3\u3064<\/h2>\n<p>\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3084\u56db\u6b21\u65b9\u7a0b\u5f0f\u306a\u3069\u3001\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u306f\u4e3b\u306b3\u3064\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u65b9\u6cd5\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u516c\u5f0f\uff08\u56e0\u6570\u5206\u89e3\u3001\u89e3\u306e\u516c\u5f0f\uff09\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b<\/li>\n<li>\u6587\u5b57\u306e\u7f6e\u304d\u63db\u3048\u3092\u3057\u3066\u8a08\u7b97\u3059\u308b<\/li>\n<li>\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u56e0\u6570\u5206\u89e3\u3059\u308b<\/li>\n<\/ul>\n<p>\u305d\u308c\u305e\u308c\u306e\u65b9\u6cd5\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u89e3\u3092\u5f97\u308b<\/h3>\n<p>\u6700\u3082\u308f\u304b\u308a\u3084\u3059\u3044\u65b9\u6cd5\u304c\u516c\u5f0f\u306e\u5229\u7528\u3067\u3059\u3002\u307e\u305a\u3001\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u56e0\u6570\u5206\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u5f8c\u3001\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u89e3\u3092\u5f97\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(x^3=8\\)<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u56e0\u6570\u5206\u89e3\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(x^3=8\\)<\/p>\n<p>\\(x^3-8=0\\)<\/p>\n<p>\\(x^3-2^3=0\\)<\/p>\n<p>\\((x-2)(x^2+2x+4)=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x=2\\)\u304c\u7b54\u3048\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u306a\u304a\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u305f\u3081\u3001\u7b54\u3048\u306f3\u3064\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\\(x^2+2x+4=0\\)\u306e\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{-2\u00b1\\sqrt{2^2-4\u00d74}}{2}\\)<\/p>\n<p>\\(x=\\displaystyle\\frac{-2\u00b1\\sqrt{12}i}{2}\\)<\/p>\n<p>\\(x=-1\u00b1\\sqrt{3}i\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(x=2\\)\u3068\\(x=-1\u00b1\\sqrt{3}i\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7f6e\u304d\u63db\u3048\u306b\u3088\u3063\u3066\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u6587\u5b57\u306e\u7f6e\u304d\u63db\u3048\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u3051\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u6587\u5b57\u306e\u7f6e\u304d\u63db\u3048\u3092\u884c\u3044\u3001\u56e0\u6570\u5206\u89e3\u3068\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u306e\u3067\u3059\u3002\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(x^4+2x^2-3=0\\)<\/li>\n<\/ul>\n<p>\\(x^2=X\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u3088\u3046\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5f0f\u306f\\(X^2+2X-3=0\\)\u3068\u306a\u308b\u306e\u3067\u56e0\u6570\u5206\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(X^2+2X-3=0\\)<\/p>\n<p>\\((X+3)(X-1)=0\\)<\/p>\n<p>\\(X=1,-3\\)\u304c\u7b54\u3048\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u7f6e\u304d\u63db\u3048\u305f\u6587\u5b57\u3092\u623b\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(x^2=1(X=1)\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(x^2=1\\)<\/p>\n<p>\\(x=\u00b11\\)<\/p>\n<p><strong>\u30fb\\(x^2=-3(X=-3)\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\\(x^2=-3\\)<\/p>\n<p>\\(x=\u00b1\\sqrt{3}i\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(x=\u00b11\\)\u3068\\(x=\u00b1\\sqrt{3}i\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u3001\u56e0\u6570\u5206\u89e3\u3092\u3059\u308b<\/h3>\n<p>\u3069\u306e\u3088\u3046\u306b\u56e0\u6570\u5206\u89e3\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u3001\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u56e0\u6570\u5206\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u30d2\u30f3\u30c8\u306a\u3057\u306b\u56e0\u6570\u5206\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u3082\u306e\u306e\u3001\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3059\u308c\u3070\u56e0\u6570\u3092\u898b\u3064\u3051\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\\(x\\)\u306b\u5024\u3092\u4ee3\u5165\u3057\u3001\u7b54\u3048\u304c0\u306b\u306a\u308c\u3070\u3001\u56e0\u6570\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span>\u4f8b\u3048\u3070\\(P(1)=0\\)\u306e\u5834\u5408\u3001\\(x=1\\)\u3067\u7b54\u3048\u304c0\u306b\u306a\u308b\u305f\u3081\u3001\\(P(x)\\)\u306f\\(x-1\\)\u3092\u56e0\u6570\u306b\u3082\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u6b21\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(x^3+3x^2+4x+4=0\\)<\/li>\n<\/ul>\n<p>\\(P(x)=x^3+3x^2+4x+4\\)\u3068\u3059\u308b\u3068\u3001\\(x\\)\u306b\u4f55\u306e\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u7b54\u3048\u304c0\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u30e9\u30f3\u30c0\u30e0\u306b\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001\\(x=-2\\)\u306e\u3068\u304d\u306b\\(P(-2)=0\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(P(x)\\)\u306f\\(x+2\\)\u3092\u56e0\u6570\u306b\u3082\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5272\u308a\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh17.jpg\" alt=\"\" width=\"450\" height=\"371\" class=\"aligncenter size-full wp-image-11165\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(P(x)=x^3+3x^2+4x+4\\)\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56e0\u6570\u5206\u89e3\u3067\u304d\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(P(x)=(x+2)(x^2+x+2)\\)<\/li>\n<\/ul>\n<p>\\(x^3+3x^2+4x+4=0\\)\u306b\u3064\u3044\u3066\u3001\u89e3\u306e\u4e00\u3064\u306f\\(x=-2\\)\u3067\u3059\u3002\u6b21\u306b\u3001\\(x^2+x+2=0\\)\u3068\u306a\u308b\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u89e3\u306e\u516c\u5f0f\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7b54\u3048\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{7}i}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(x=-2\\)\u3068\\(x=\\displaystyle\\frac{-1\u00b1\\sqrt{7}i}{2}\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7f6e\u304d\u63db\u3048\u3084\u56e0\u6570\u5b9a\u7406\u3092\u884c\u3048\u306a\u3044\u5834\u5408\u306e\u8a08\u7b97\u65b9\u6cd5<\/h3>\n<p>\u306a\u304a\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u7f6e\u304d\u63db\u3048\u3084\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3067\u304d\u306a\u3044\u30b1\u30fc\u30b9\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5e73\u65b9\u306e\u5dee\u306b\u7740\u76ee\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001<span style=\"color: #ff0000;\">\u7121\u7406\u3084\u308a\u4e8c\u4e57\u306e\u5f62\u3092\u4f5c\u308b\u306e\u3067\u3059\u3002<\/span>\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(x^4+x^2+4=0\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5f0f\u3067\u306f\u3001\u6587\u5b57\u306e\u7f6e\u304d\u63db\u3048\u3092\u3057\u3066\u3082\u3001\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u3066\u3082\u554f\u984c\u3092\u89e3\u3051\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u4e8c\u4e57\u306e\u5f62\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\u5f0f\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\\((x^2+2)^2\\)\u3067\u3042\u308c\u3070\u3001\u4f3c\u305f\u5f0f\u3092\u4f5c\u308c\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u3001\u3064\u3058\u3064\u307e\u3092\u5408\u308f\u305b\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\\((x^2+2)^2=x^4+4x^2+4\\)\u3067\u3042\u308b\u305f\u3081\u3001\u5143\u306e\u5f0f\u3088\u308a\u3082\\(3x^2\\)\u304c\u591a\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(3x^2\\)\u3092\u5f15\u304d\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<p>\\((x^2+2)^2-3x^2=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x^4+x^2+4=0\\)\u3092\\((x^2+2)^2-3x^2=0\\)\u3078\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u3053\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\u3001\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\\(a^2-b^2=(a+b)(a-b)\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56e0\u6570\u5206\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((x^2+2)^2-3x^2=0\\)<\/p>\n<p>\\((x^2+2+\\sqrt{3}x)(x^2+2-\\sqrt{3}x)=0\\)<\/p>\n<p>\\((x^2+\\sqrt{3}x+2)(x^2-\\sqrt{3}x+2)=0\\)<\/p>\n<p>\u6b21\u306b\u3001\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\\(x^2+\\sqrt{3}x+2=0\\)\u3068\\(x^2-\\sqrt{3}x+2=0\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{-\\sqrt{3}\u00b1\\sqrt{5}i}{2}\\)<\/p>\n<p>\\(x=\\displaystyle\\frac{\\sqrt{3}\u00b1\\sqrt{5}i}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u30014\u3064\u306e\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u6b21\u6570\u3092\u4e0b\u3052\u3001\u8a08\u7b97\u3092\u7c21\u5358\u306b\u3059\u308b<\/h2>\n<p>\u306a\u304a\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u3067\u306f\u3001\u6b21\u6570\u304c\u5927\u304d\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u5834\u5408\u3001\u6b21\u6570\u3092\u4e0b\u3052\u308b\u3053\u3068\u3067\u8a08\u7b97\u3092\u7c21\u5358\u306b\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3067\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(f(x)=x^{2000}\\)\u3068\u3057\u307e\u3059\u3002\\(x^2+x+1=0\\)\u306e\u89e3\u306e\u4e00\u3064\u304c\u03c9\u306e\u3068\u304d\u3001\\(f(\u03c9)\\)\u306e\u5024\u3092\u4e00\u6b21\u5f0f\u3067\u8a18\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(x^2+x+1=0\\)\u306e\u89e3\u306e\u4e00\u3064\u304c\u03c9\u3067\u3042\u308b\u305f\u3081\u3001\\(\u03c9^2+\u03c9+1=0\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03c9^2+\u03c9=-1\\)<\/li>\n<li>\\(\u03c9^2=-\u03c9-1\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\\(\u03c9^3\\)\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\u03c9^3\\)<\/p>\n<p>\\(=\u03c9\u00b7\u03c9^2\\)<\/p>\n<p>\\(=\u03c9(-\u03c9-1)\\)<\/p>\n<p>\\(=-(\u03c9^2+\u03c9)\\)<\/p>\n<p>\\(=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(\u03c9^3=1\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(f(\u03c9)=\u03c9^{2000}\\)<\/p>\n<p>\\(f(\u03c9)=\u03c9^{3\u00d7666}\u00b7\u03c9^2\\)<\/p>\n<p>\\(f(\u03c9)=1^{666}\u00b7(-\u03c9-1)\\)<\/p>\n<p>\\(f(\u03c9)=-\u03c9-1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(f(\u03c9)=-\u03c9-1\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u4e8c\u91cd\u89e3\u3092\u3082\u3064\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u6761\u4ef6<\/h3>\n<p>\u6b21\u306b\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u304c\u4e8c\u91cd\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u3001\u4e8c\u91cd\u89e3\uff08\u307e\u305f\u306f\u4e09\u91cd\u89e3\uff09\u3092\u3082\u3064\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u304c\\(a\\)\u3068\\(b\\)\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306f\u4e8c\u91cd\u89e3\u3092\u3082\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=(x-a)^2(x-b)\\)<\/li>\n<li>\\(f(x)=(x-a)(x-b)^2\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u3001\\(f(x)=(x-a)^3\\)\u3067\u8868\u3059\u3053\u3068\u306e\u3067\u304d\u308b\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306f\u4e09\u91cd\u89e3\u3092\u3082\u3061\u307e\u3059\u3002\u3053\u3046\u3057\u305f\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(f(x)=2x^3+ax^2+bx+3\\)\u306b\u3064\u3044\u3066\u3001\\(a\\)\u3068\\(b\\)\u306f\u5b9f\u6570\u3067\u3059\u3002\\(x=-1\\)\u3067\u91cd\u89e3\u3068\u306a\u308b\u3068\u304d\u3001\\(a\\)\u3001\\(b\\)\u3001\u304a\u3088\u3073\\(x=-1\\)\u4ee5\u5916\u306e\u7b54\u3048\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(x=-1\\)\u4ee5\u5916\u306e\u7b54\u3048\u3092\\(p\\)\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=2(x+1)^2(x-p)\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u5148\u307b\u3069\u306e\u5f0f\u3092\u5c55\u958b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(f(x)=2(x+1)^2(x-p)\\)<\/p>\n<p>\\(f(x)=2(x^2+2x+1)(x-p)\\)<\/p>\n<p>\\(f(x)=2(x^3-px^2+2x^2-2px+x-p)\\)<\/p>\n<p>\\(f(x)=2x^3+(4-2p)x^2+(2-4p)x\\)\\(-2p\\)<\/p>\n<p>\u4fc2\u6570\u306f\u4e00\u81f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\\(f(x)=2x^3+ax^2+bx+3\\)\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(4-2p=a\\)<\/li>\n<li>\\(2-4p=b\\)<\/li>\n<li>\\(-2p=3\\)<\/li>\n<\/ul>\n<p>\\(-2p=3\\)\u3088\u308a\u3001\\(p=-\\displaystyle\\frac{3}{2}\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(x=-1\\)\u4ee5\u5916\u306e\u7b54\u3048\u306f\\(x=-\\displaystyle\\frac{3}{2}\\)\u3067\u3059\u3002\u307e\u305f\\(p=-\\displaystyle\\frac{3}{2}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=7\\)\u3001\\(b=8\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2<\/h2>\n<p>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u4e2d\u3067\u3082\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3067\u306f\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5b66\u3073\u307e\u3059\u3002\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3067\u91cd\u8981\u306a\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3067\u3059\u304c\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306b\u3082\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u304c\u3042\u308b\u306e\u3067\u3059\u3002\u306a\u304a\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5b66\u3079\u3070\u3001\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306e\u4e09\u6b21\u65b9\u7a0b\u5f0f\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(ax^3+bx^2+cx+d=0\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\\(\u03b1\\)\u3001\\(\u03b2\\)\u3001\\(\u03b3\\)\u3068\u3059\u308b\u3068\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03b1+\u03b2+\u03b3=-\\displaystyle\\frac{b}{a}\\)<\/li>\n<li>\\(\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1=\\displaystyle\\frac{c}{a}\\)<\/li>\n<li>\\(\u03b1\u03b2\u03b3=-\\displaystyle\\frac{d}{a}\\)<\/li>\n<\/ul>\n<p>\u8a3c\u660e\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u89e3\u304c\\(\u03b1\\)\u3001\\(\u03b2\\)\u3001\\(\u03b3\\)\u3067\u3042\u308b\u306a\u3089\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56e0\u6570\u5206\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(ax^3+bx^2+cx+d\\)<\/p>\n<p>\\(=a(x-\u03b1)(x-\u03b2)(x-\u03b3)\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u3092\u5c55\u958b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a(x-\u03b1)(x-\u03b2)(x-\u03b3)\\)<\/p>\n<p>\\(=a(x^2-(\u03b1+\u03b2)x+\u03b1\u03b2)(x-\u03b3)\\)<\/p>\n<p>\\(=a(x^3-(\u03b1+\u03b2+\u03b3)x^2\\)\\(+(\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1)x\\)\\(-\u03b1\u03b2\u03b3)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u4fc2\u6570\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001\u5148\u307b\u3069\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5fd8\u308c\u305f\u3068\u3057\u3066\u3082\u3001\u56e0\u6570\u5b9a\u7406\u306b\u3088\u308b\u8a3c\u660e\u65b9\u6cd5\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001\u516c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u53c2\u8003\u307e\u3067\u306b\u3001<span style=\"color: #0000ff;\">\u56db\u6b21\u65b9\u7a0b\u5f0f\u3067\u3082\u540c\u3058\u3088\u3046\u306b\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span>\u56db\u6b21\u65b9\u7a0b\u5f0f\\(ax^4+bx^3+cx^2+dx+e=0\\)\u306e\u89e3\u3092\\(\u03b1\\)\u3001\\(\u03b2\\)\u3001\\(\u03b3\\)\u3001\\(\u03b4\\)\u3068\u3059\u308b\u3068\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03b1+\u03b2+\u03b3+\u03b4=-\\displaystyle\\frac{b}{a}\\)<\/li>\n<li>\\(\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b4+\u03b4\u03b1+\u03b1\u03b3+\u03b2\u03b3\\)\\(=\\displaystyle\\frac{c}{a}\\)<\/li>\n<li>\\(\u03b1\u03b2\u03b3+\u03b2\u03b3\u03b4+\u03b3\u03b4\u03b1+\u03b4\u03b1\u03b2=-\\displaystyle\\frac{d}{a}\\)<\/li>\n<li>\\(\u03b1\u03b2\u03b3\u03b4=\\displaystyle\\frac{e}{a}\\)<\/li>\n<\/ul>\n<p>\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u3053\u306e\u95a2\u4fc2\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u5bfe\u79f0\u5f0f\u306e\u7b54\u3048\u3092\u5f97\u308b<\/h3>\n<p>\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u6570\u5b66\u306e\u554f\u984c\u3092\u89e3\u3051\u308b\u30b1\u30fc\u30b9\u306f\u591a\u3044\u3067\u3059\u3002\u5bfe\u79f0\u5f0f\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u304c\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\\(3x^3-6x^2-9x+1=0\\)\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\u89e3\u3092\\(\u03b1\\)\u3001\\(\u03b2\\)\u3001\\(\u03b3\\)\u3068\u3059\u308b\u3068\u3001\\(\u03b1^2+\u03b2^2+\u03b3^2\\)\u306e\u5024\u306f\u3069\u3046\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\u03b1+\u03b2+\u03b3=2\\)<\/li>\n<li>\\(\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1=-3\\)<\/li>\n<li>\\(\u03b1\u03b2\u03b3=-\\displaystyle\\frac{1}{3}\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\\(\u03b1^2+\u03b2^2+\u03b3^2\\)\u3092\u5909\u5f62\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\u03b1^2+\u03b2^2+\u03b3^2\\)<\/p>\n<p>\\(=(\u03b1+\u03b2+\u03b3)^2-2(\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1)\\)<\/p>\n<p>\\(=2^2-2\u00d7-3\\)<\/p>\n<p>\\(=10\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f10\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u306a\u304a\u5bfe\u79f0\u5f0f\u306b\u9650\u3089\u305a\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3067\u304d\u308b\u5834\u9762\u306f\u591a\u3044\u3067\u3059\u3002<\/p>\n<h2>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u304c\u95a2\u308f\u308b\u554f\u984c\u3092\u89e3\u304f<\/h2>\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3088\u308a\u3082\u8a08\u7b97\u304c\u8907\u96d1\u306b\u306a\u308a\u3084\u3059\u3044\u554f\u984c\u304c\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3084\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306b\u306f\u3001\u516c\u5f0f\u3084\u7f6e\u304d\u63db\u3048\u3001\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u516c\u5f0f\u3084\u56e0\u6570\u5b9a\u7406\u3092\u5229\u7528\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u3042\u308b\u3082\u306e\u306e\u3001\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u3067\u306f\u3001\u6b21\u6570\u3092\u4e0b\u3052\u305f\u308a\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u305f\u308a\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u3092\u5229\u7528\u3057\u306a\u3044\u5834\u5408\u3001\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u306f\u8907\u96d1\u3067\u3059\u3002\u305d\u3053\u3067\u8a08\u7b97\u3092\u7c21\u5358\u306b\u3059\u308b\u305f\u3081\u306e\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u306b\u306f\u89e3\u304d\u65b9\u304c\u3042\u308a\u307e\u3059\u3002\u4e09\u6b21\u65b9\u7a0b\u5f0f\u3084\u56db\u6b21\u65b9\u7a0b\u5f0f\u306b\u95a2\u308f\u308b\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304d\u3001\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u79c1\u305f\u3061\u304c\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u591a\u304f\u306f\u4e00\u6b21\u65b9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