\\(m\\) \u3092\u6574\u6570\u3068\u3057, \\(f(x) = x^3+8x^2+mx+60\\) \u3068\u3059\u308b.<\/p>\r\n
(1)<\/strong>\u3000\u6574\u6570 \\(a\\) \u3068, \\(0\\) \u3067\u306f\u306a\u3044\u6574\u6570 \\(b\\) \u3067, \\(f(a+bi) = 0\\) \u3092\u307f\u305f\u3059\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3088\u3046\u306a \\(m\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088. \u305f\u3060\u3057, \\(i\\) \u306f\u865a\u6570\u5358\u4f4d\u3067\u3042\u308b.<\/p><\/li>\r\n (2)<\/strong>\u3000(1)<\/strong> \u3067\u6c42\u3081\u305f\u3059\u3079\u3066\u306e \\(m\\) \u306b\u5bfe\u3057\u3066, \u65b9\u7a0b\u5f0f \\(f(x) = 0\\) \u3092\u89e3\u3051.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \u6761\u4ef6\u3088\u308a, \\(f(x) = 0\\) \u306e \\(3\\) \u3064\u306e\u89e3\u306f, \u5b9f\u6570 \\(c\\) \u3092\u7528\u3044\u3066 \\(x= a \\pm bi , c\\) \u3068\u8868\u305b\u308b. (2)<\/strong><\/p>\r\n (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070, \u6c42\u3081\u308b\u89e3\u306f<\/p>\r\n
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n
\r\n\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308b\u3068\r\n\\[\\begin{align}\r\n2a+c & = -8 \\quad ... [1] \\ , \\\\\r\na^2+b^2 +2ac & = m \\quad ... [2] \\ , \\\\\r\nc(a^2+b^2) & = -60 \\quad ... [3]\r\n\\end{align}\\]\r\n[1] \u3088\u308a, \\(c\\) \u3082\u6574\u6570\u3067\u3042\u308a\r\n\\[\r\nc = -2(a+4) \\quad ... [4]\r\n\\]\r\n[3] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\r\n(a+4)(a^2+b^2) = 30\r\n\\]\r\n\u3053\u3053\u3067, \\(30 = 2 \\cdot 3 \\cdot 5\\) \u306e\u7d04\u6570\u306e\u3046\u3061, \\(2\\) \u3064\u306e\u5e73\u65b9\u6570\u306e\u548c\u3067\u8868\u305b\u308b\u306e\u306f \\(1 , 2 , 5 , 10\\) \u306e\u307f\u306a\u306e\u3067, \\(a , a^2+b^2\\) \u306e\u53d6\u308a\u5f97\u308b\u5024\u306f\r\n\\[\r\n( a , a^2 +b^2 ) = ( 26 , 1 ) , ( 11 , 2 ) , ( 2 , 5 ) , ( -1 , 10 )\r\n\\]\r\n\u3053\u306e\u3046\u3061, \\(a , b\\) \u3068\u3082\u306b\u6574\u6570\u3068\u306a\u308b\u306e\u306f\r\n\\[\r\n(a,b) = ( 2 , \\pm 1 ) , (-1 , \\pm 3 )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [2] [4]\u3092\u7528\u3044\u3066<\/p>\r\n\r\n
\r\n\\[\\begin{align}\r\nc & = -2 (2+4) = -12 \\ , \\\\\r\nm & = 5 +2 \\cdot 2 \\cdot (-12) = -43\r\n\\end{align}\\]<\/li>\r\n
\r\n\\[\\begin{align}\r\nc & = -2 (-1+4) = -6 \\ , \\\\\r\nm & = 10 +2 \\cdot (-1) \\cdot (-6) = 22\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b \\(m\\) \u306e\u5024\u306f\r\n\\[\r\nm = \\underline{-43 , 22}\r\n\\]<\/li>\r\n<\/ul>\r\n\r\n
\r\n\\[\r\nx = \\underline{2 \\pm i , -12}\r\n\\]<\/li>\r\n
\r\n\\[\r\nx = \\underline{-1 \\pm 3i , -6}\r\n\\]<\/li>\r\n<\/ul>\r\n","protected":false},"excerpt":{"rendered":"\\(m\\) \u3092\u6574\u6570\u3068\u3057, \\(f(x) = x^3+8x^2+mx+60\\) \u3068\u3059\u308b. (1)\u3000\u6574\u6570 \\(a\\) \u3068, \\(0\\) \u3067\u306f\u306a\u3044\u6574\u6570 \\(b\\) \u3067, \\(f(a+bi) = 0\\) \u3092\u307f\u305f\u3059\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3088 … \u7d9a\u304d\u3092\u8aad\u3080