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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Resolvent cubic ： ウィキペディア英語版 Resolvent cubic In mathematics, a resolvent cubic polynomial is defined as follows: Let :$f(x)=x^4+a\_3x^3+a\_2x^2+a\_1x+a\_0\; \backslash ,$ be a monic quartic polynomial. The ''resolvent cubic'' is the monic cubic polynomial :$g(x)=\; x^3+b\_2x^2+b\_1x+b\_0\; \backslash ,$ where :$b\_2\; =\; -a\_2\; \backslash ,$ :$b\_1\; =\; a\_1a\_3\; -\; 4a\_0\; \backslash ,$ :$b\_0\; =\; 4a\_0a\_2\; -\; a\_1^2\; -a\_0a\_3^2.\; \backslash ,$ This can be used to find the roots of the quartic, by using the following relations between the roots $\backslash alpha\_i$ of ''f'' and the roots $\backslash beta\_i$ of ''g'': :$\backslash beta\_1\; =\; \backslash alpha\_1\; \backslash alpha\_2\; +\; \backslash alpha\_3\; \backslash alpha\_4$ :$\backslash beta\_2\; =\; \backslash alpha\_1\; \backslash alpha\_3\; +\; \backslash alpha\_2\; \backslash alpha\_4$ :$\backslash beta\_3\; =\; \backslash alpha\_1\; \backslash alpha\_4\; +\; \backslash alpha\_2\; \backslash alpha\_3.$ These can be established simply with Vieta's formulas. ==See also== *Resolvent (Galois theory) *Zero of a function 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Resolvent cubic」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.