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關(guān)于整系數(shù)多項(xiàng)式的根的若干性質(zhì)
關(guān)于整系數(shù)多項(xiàng)式的根的若干性質(zhì)
摘要：本文論述了關(guān)于整系數(shù)多項(xiàng)式的根的若干性質(zhì)。包括整系數(shù)多項(xiàng)式的無(wú)整數(shù)根的充分性，整系數(shù)多項(xiàng)式無(wú)重根的充分性。提到了3種對(duì)于整系數(shù)多項(xiàng)式f(x)=a0xn+a1xn-1+… + amxm+… +an-1x+an，（a0≠0）的有理根的檢驗(yàn)范圍進(jìn)行縮小的方法。并對(duì)整系數(shù)多項(xiàng)式的最高次系數(shù)和常數(shù)項(xiàng)的因子比較多，有理根的檢驗(yàn)比較復(fù)雜的情況，文章給出了幾個(gè)命題，根據(jù)整系數(shù)多項(xiàng)式系數(shù)所滿足的條件，判斷相應(yīng)的整系數(shù)多項(xiàng)式是否存在有理根，使某些類型的整系數(shù)多項(xiàng)式的檢定更為方便。
關(guān)鍵詞：整系數(shù)多項(xiàng)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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