整系數多項式的根的若干性質

關于整系數多項式的根的若干性質

關于整系數多項式的根的若干性質
   
 
  摘要：本文論述了關于整系數多項式的根的若干性質。包括整系數多項式的無整數根的充分性，整系數多項式無重根的充分性。提到了3種對于整系數多項式f(x)=a0xn+a1xn-1+… + amxm+… +an-1x+an，（a0≠0）的有理根的檢驗范圍進行縮小的方法。并對整系數多項式的最高次系數和常數項的因子比較多，有理根的檢驗比較復雜的情況，文章給出了幾個命題，根據整系數多項式系數所滿足的條件，判斷相應的整系數多項式是否存在有理根，使某些類型的整系數多項式的檢定更為方便。
關鍵詞：整系數多項式；有理根；判定；范圍

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

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