| 整系数多项式有理根一个新求法的再探讨 |
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| 引用本文： | 朱玉扬. 整系数多项式有理根一个新求法的再探讨[J]. 数学的实践与认识, 2005, 35(5): 229-232 |
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| 作者姓名： | 朱玉扬 |
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| 作者单位： | 合肥学院数学与物理系,安徽,合肥,230022 |
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| 摘 要： | 设f (x)为整系数多项式,α为有理数,对n个不同的整数t1,…,tn,gα(tk) =f (tk)tk-α都是整数,那么α是f (x)的根的充要条件是f (t) =∑ni=1∏1≤j≤nj≠it-tjti-tjgα(ti) ( t∈Z) .
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| 关 键 词： | 整系数多项式 有理根 Lagrange插值公式 |
| 修稿时间： | 2001-03-06 |
Further Study of a new Method for Finding Roots of Integral Coefficient Polynomials |
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| ZHU Yu-yang. Further Study of a new Method for Finding Roots of Integral Coefficient Polynomials[J]. Mathematics in Practice and Theory, 2005, 35(5): 229-232 |
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| Authors: | ZHU Yu-yang |
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| Abstract: | Define f(x) an integral coefficient polynoial, α a rational number and g α(t k)=f(t k)t k-α to be an integral number. For n different integral numbers t 1, …, t n, the necessary and sufficient condition of α being a root of f(x) is that f(t)=∑ni=1 ∏1≤j≤nj≠it-t jt i-t jg α(t i) (t∈Z). |
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| Keywords: | integral coefficient polynomials rational roots Lagrange interpolating formula |
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