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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 Hudde's rules ： ウィキペディア英語版 Hudde's rules In mathematics, Hudde's rules are two properties of polynomial roots described by Johann Hudde. 1. If ''r'' is a double root of the polynomial equation ::$a\_0x^n\; +\; a\_1x^\; +\; \backslash cdots\; +\; a\_x\; +\; a\_n\; =\; 0\; \backslash ,$ :and if $b\_0,\; b\_1,\; \backslash dots,\; b\_,\; b\_n$ are numbers in arithmetic progression, then ''r'' is also a root of ::$a\_0b\_0x^n\; +\; a\_1b\_1x^\; +\; \backslash cdots\; +\; a\_b\_x\; +\; a\_nb\_n\; =\; 0.\; \backslash ,$ :This definition is a form of the modern theorem that if ''r'' is a double root of ''ƒ''(''x'') = 0, then ''r'' is a root of ''ƒ'' '(''x'') = 0. 2. If for ''x'' = ''a'' the polynomial ::$a\_0x^n\; +\; a\_1x^\; +\; \backslash cdots\; +\; a\_x\; +\; a\_n\; \backslash ,$ :takes on a relative maximum or minimum value, then ''a'' is a root of the equation ::$na\_0x^n\; +\; (n-1)a\_1x^\; +\; \backslash cdots\; +\; 2a\_x^2\; +\; a\_x\; =\; 0.\; \backslash ,$ :This definition is a modification of Fermat's theorem in the form that if ''ƒ''(''a'') is a relative maximum or minimum value of a polynomial ''ƒ''(''x''), then ''ƒ'' '(''a'') = 0. ==References== *Carl B. Boyer, A history of mathematics, 2nd edition, by John Wiley & Sons, Inc., page 373, 1991. 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「Hudde's rules」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.