{"id":97411,"date":"2024-03-28T14:40:02","date_gmt":"2024-03-28T14:40:02","guid":{"rendered":"https:\/\/science-hub.click\/%E5%A4%9A%E9%A0%85%E5%BC%8F%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-03-28T14:40:02","modified_gmt":"2024-03-28T14:40:02","slug":"%E5%A4%9A%E9%A0%85%E5%BC%8F%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=97411","title":{"rendered":"\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u591a\u9805\u5f0f\u306f<\/b>\u6b21\u306e\u5f62\u5f0f\u306e\u65b9\u7a0b\u5f0f\u3067\u3059\u3002 <\/p>

$$ { \\qquad a_n x^n + a_{n – 1} x^{n – 1} + \\cdots + a_1 x + a_0 = 0,} $$<\/div><\/dd><\/dl>

\u3069\u3053\u3067

$$ {a_i \\!} $$<\/div> \u3001\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570<\/i>\u3068\u547c\u3070\u308c\u308b\u3001\u304c\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002\u4fc2\u6570\u306f\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u5b9f\u6570\u307e\u305f\u306f\u8907\u7d20\u6570\u3067\u3059\u304c\u3001\u3069\u306e\u74b0\u3067\u3082\u305d\u306e\u5024\u3092\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

\u6570\u5b66<\/a><\/span>\u3067\u306f\u3001\u591a\u9805\u5f0f\u306f<\/a><\/span>\u65b9\u7a0b\u5f0f\u7406\u8ad6<\/a><\/span>\u306e\u4e2d\u5fc3\u7684\u306a\u4e3b\u984c\u3067\u3059\u3002\u65b9\u7a0b\u5f0f\u7406\u8ad6<\/a><\/span>\u306e\u76ee\u6a19\u306f\u3001\u591a\u9805\u5f0f<\/a><\/span>\u306e\u6839\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u591a\u9805\u5f0f\u3092\u89e3\u304f\u306e\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306f\u3001\u672a\u77e5<\/i>\u306e\u5024\u306e\u30bb\u30c3\u30c8\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002

$$ {x \\!} $$<\/div> (\u7279\u5b9a\u306e\u30bb\u30c3\u30c8\u306b\u5c5e\u3057\u3001\u901a\u5e38\u306f\u4fc2\u6570\u3068\u540c\u3058\u672c\u4f53\u307e\u305f\u306f\u30ea\u30f3\u30b0)\u3001\u65b9\u7a0b\u5f0f\u306e\u89e3<\/i>\u3068\u547c\u3070\u308c\u3001\u591a\u9805\u65b9\u7a0b\u5f0f\u304c\u771f\u3067\u3059\u3002<\/p>

\u65b9\u7a0b\u5f0f\u306e\u6b21\u6570\u3092<\/i>\u3001\u30bc\u30ed\u4ee5\u5916\u306e\u4fc2\u6570<\/a><\/span>\u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u672a\u77e5\u6570\u306e\u6700\u5927\u7d2f\u4e57<\/a><\/span>\u3068\u547c\u3073\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f

$$ {x^2 + 2x + 1 = 0 \\!} $$<\/div>\u672a\u77e5\u306e
$$ {x \\in \\mathbb R} $$<\/div>\u306f\u5b9f\u6570\u306e 2 \u6b21\u591a\u9805\u5f0f\u3067\u3059\u3002 (\u4e00\u610f\u306e\u89e3(\u4e8c\u91cd\u89e3)\u306f\u22121<\/span>\u3067\u3059\u3002)<\/p>
\n\"\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u7406\u8ad6<\/h2>

\u591a\u9805\u5f0f<\/span><\/h3>

\u65b9\u7a0b\u5f0f\u3092\u7acb\u3066\u3066\u307f\u307e\u3057\u3087\u3046<\/p>

$$ {(\\mathrm E) \\qquad a_n x^n + a_{n – 1} x^{n – 1} + \\cdots + a_1 x + a_0 = 0,} $$<\/div><\/dd><\/dl>

\u305d\u306e\u4fc2\u6570a<\/i> i \u306f<\/i><\/sub><\/span>\u30d5\u30a3\u30fc\u30eb\u30c9\u306b\u5c5e\u3057\u307e\u3059

$$ {\\mathbb K} $$<\/div> \u3002\u306e(E)\u306e\u89e3\u6c7a\u7b56
$$ {\\mathbb K} $$<\/div>\u591a\u9805\u5f0f\u306e\u6839\u3067\u3059<\/p>
$$ {P = a_n X^n + a_{n – 1} X^{n – 1} + \\cdots + a_1 X + a_0 \\quad \\in \\mathbb K[X],} $$<\/div><\/dd><\/dl>

\u4e0d\u5b9a\u306e<\/a><\/span>x \u3092<\/i><\/span>\u672a\u77e5\u306ex<\/i><\/span>\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>

\u4ee3\u6570<\/a><\/span>\u3067\u306f\u3001 n<\/i><\/span>\u6b21\u306e\u591a\u9805\u5f0f\u306b\u306f\u6700\u5927\u3067\u3082n \u500b<\/i><\/span>\u306e\u6839\u304c\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u65b9\u7a0b\u5f0f (E) \u306f\u6700\u5927n \u500b<\/i><\/span>\u306e\u89e3\u3092\u8a31\u5bb9\u3057\u307e\u3059\u3002<\/p>

\u3082\u3057

$$ {\\mathbb K’} $$<\/div>\u306e\u8d85\u4f53\u3067\u3059
$$ {\\mathbb K} $$<\/div> \u3001 (E) \u3092\u6b21\u306e\u4fc2\u6570\u3092\u6301\u3064\u65b9\u7a0b\u5f0f\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002
$$ {\\mathbb K’} $$<\/div> ;\u304a\u3088\u3073 (E) \u306e\u89e3\u6c7a\u7b56
$$ {\\mathbb K} $$<\/div>\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3067\u3082\u3042\u308a\u307e\u3059
$$ {\\mathbb K’} $$<\/div> (\u305d\u306e\u9006\u306f\u4e00\u822c\u306b\u8aa4\u308a\u3067\u3059)\u3002\u306e\u30aa\u30fc\u30d0\u30fc\u30dc\u30c7\u30a3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u3044\u3064\u3067\u3082\u53ef\u80fd\u3067\u3059
$$ {\\mathbb K} $$<\/div> \u3001\u591a\u9805\u5f0fP<\/i><\/span>\u306e\u5206\u89e3\u672c\u4f53\u3068\u547c\u3070\u308c\u3001(E) \u306f\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u306e\u89e3\u3092\u8a31\u5bb9\u3057\u307e\u3059\u3002<\/p>
\n\"\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u5b9f\u6570\u5f0f\u304a\u3088\u3073\u8907\u7d20\u6570\u5f0f\u306e\u89e3\u306e\u5b58\u5728<\/span><\/h3>

\u30c0\u30e9\u30f3\u30d9\u30fc\u30eb-\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u306f<\/span>\u3001\u8907\u7d20\u4f53\u306f\u4ee3\u6570\u7684\u306b\u9589\u3058\u3066\u3044\u308b\u3001\u3064\u307e\u308a\u8907\u7d20\u4fc2\u6570\u3092\u6301\u3061\u3001\u6b21\u6570\u304c\u5c11\u306a\u304f\u3068\u3082 1 \u3064\u3042\u308b\u591a\u9805\u5f0f\u306f\u89e3\u3092\u53d7\u3051\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u5b9f\u4fc2\u6570\u3092\u6301\u3064 1 \u6b21\u4ee5\u4e0a\u306e\u591a\u9805\u5f0f\u306f\u8907\u7d20<\/i>\u89e3\u3092\u8a31\u5bb9\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001 x<\/i> 2<\/sup> + 1 = 0<\/span>\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u306b\u306f\u89e3\u304c\u3042\u308a\u307e\u305b\u3093\u3002

$$ {\\mathbb R } $$<\/div> (\u305d\u306e\u89e3\u306f\u8907\u7d20\u6570i<\/i><\/span>\u3068\u2212 i<\/i><\/span>\u3067\u3059)\u3002<\/p>

\u5b9f\u6570\u5f0f<\/a><\/span>P<\/i>\u306e\u5b9f\u6570\u89e3\u306e\u76f4\u89b3\u3068\u540c\u69d8\u306b\u3001<\/i><\/span>\u8907\u96d1\u306a\u5b9f\u6570\u5f0f\u306f\u9a5a\u304f\u3079\u304d\u3082\u306e\u3067\u3042\u308a\u3001\u305d\u306e\u4f4d\u7f6e\u304c\u76f4\u89b3\u7684\u306b\u306f\u6c7a\u5b9a\u3067\u304d\u306a\u3044\u3088\u3046\u306b\u898b\u3048\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>

\u305f\u3060\u3057\u3001\u5947\u6570\u6b21\u306e\u5b9f\u591a\u9805\u65b9\u7a0b\u5f0f\u306f\u5fc5\u7136\u7684\u306b\u5b9f\u6570\u89e3\u3092\u8a8d\u3081\u307e\u3059\u3002\u5b9f\u969b\u3001\u95a2\u9023\u3059\u308b\u591a\u9805\u5f0f\u95a2\u6570\u306f<\/a><\/span>\u9023\u7d9a\u7684\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306a\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002

$$ {-\\infty} $$<\/div>\u306e\u8fd1\u304f\u3067
$$ {-\\infty} $$<\/div>\u305d\u3057\u3066\u5411\u304b\u3063\u3066
$$ {+\\infty} $$<\/div>\u306e\u8fd1\u304f\u3067
$$ {+\\infty} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4e2d\u9593\u5024\u306e\u5b9a\u7406\u306b\u3088\u308c\u3070\u3001\u7279\u5b9a\u306e\u5b9f\u6570\u3067\u306f\u5024 0 \u304c\u53d6\u3089\u308c\u3001\u3053\u308c\u304c\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u306a\u308a\u307e\u3059\u3002<\/p>

\u30ac\u30ed\u30a2\u7406\u8ad6<\/a><\/span>\u3068\u306e\u30ea\u30f3\u30af<\/span><\/h3>

\u4fc2\u6570\u306e\u95a2\u6570\u3068\u3057\u3066\u6b21\u6570\u304c 4 \u4ee5\u4e0b\u306e\u5b9f\u6570\u307e\u305f\u306f\u8907\u7d20\u591a\u9805\u5f0f\u306e\u89e3\u3092\u4e0e\u3048\u308b\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u30a2\u30fc\u30d9\u30eb\u306f\u30015 \u6b21\u4ee5\u4e0a\u306e\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u306f (\u901a\u5e38\u306e 4 \u3064\u306e\u6f14\u7b97\u3068\u6839\u3060\u3051\u3092\u4f7f\u7528\u3057\u3066) \u3053\u306e\u3088\u3046\u306a\u4e00\u822c\u5f0f\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u30ac\u30ed\u30a2\u7406\u8ad6\u306f\u3001\u591a\u9805\u65b9\u7a0b\u5f0f\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306b<\/span>\u3001\u305d\u306e\u89e3\u304c\u6839\u53f7\u3067\u8868\u73fe\u3055\u308c\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306e\u57fa\u6e96\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u0645\u0639\u0627\u062f\u0644\u0629 \u062c\u0628\u0631\u064a\u0629 \u2013 arabe<\/a><\/li>
  2. \u0410\u043b\u0433\u0435\u0431\u0440\u0430\u0456\u0447\u043d\u0430\u0435 \u045e\u0440\u0430\u045e\u043d\u0435\u043d\u043d\u0435 \u2013 bi\u00e9lorusse<\/a><\/li>
  3. \u09ac\u09b9\u09c1\u09aa\u09a6\u09c0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u2013 bengali<\/a><\/li>
  4. Polynomick\u00e1 rovnice \u2013 tch\u00e8que<\/a><\/li>
  5. \u0410\u043b\u0433\u0435\u0431\u0440\u0103\u043b\u043b\u0430 \u0442\u0430\u043d\u043b\u0103\u0445 \u2013 tchouvache<\/a><\/li>
  6. Algebraische Gleichung \u2013 allemand<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n