关于整系数多项式的根的若干性质

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翻新时间：2013-12-18

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关于整系数多项式的根的若干性质

摘要：本文论述了关于整系数多项式的根的若干性质。包括整系数多项式的无整数根的充分性，整系数多项式无重根的充分性。提到了3种对于整系数多项式f(x)=a0xn+a1xn-1+… + amxm+… +an-1x+an，（a0≠0）的有理根的检验范围进行缩小的方法。并对整系数多项式的最高次系数和常数项的因子比较多，有理根的检验比较复杂的情况，文章给出了几个命题，根据整系数多项式系数所满足的条件，判断相应的整系数多项式是否存在有理根，使某些类型的整系数多项式的检定更为方便。

关键词：整系数多项式；有理根；判定；范围

SOME PROPERTIES OF ROOT OF POLYNOMIAL WITH INTEGER COEFICIENT

Mathematics and Applied Mathematics Dngshangzhe Instructors Lujinwang

Abstract ：The paper discusses some properties of root of polynomial with integer coeficient．For example，suficient of polynomials with integer coefficient is not integer root and is not repeated complex root etc.And about integral coefficient polynomial,f(x)=a0xn+a1xn-1+… + amxm+… +an-1x+an，，（a0≠0）,of rational root which is range have been reducing.Then we obtains some theorems which can be used to prove that the multinomials with rational coefficients do not contain rational roots，considering the conditions of the coeficient of those discrimination . it is more convenient to test some rational root of the integral coefficents polynomials than other methods．

Key words： integral coefficicents polynomial ; rational root ; discrimination;range