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单词 RationalRootTheorem
释义

rational root theorem


Consider the polynomialPlanetmathPlanetmath

p(x)=anxn+an-1xn-1++a1x+a0

where all the coefficients ai are integers.

If p(x) has a rational zero u/v where  gcd(u,v)=1,  then ua0  and  van.  Thus, for finding all rational zeros of p(x), it suffices to perform a finite number of tests.

The theorem is related to the result about monic polynomials whose coefficients belong to a unique factorization domainMathworldPlanetmath. Such theorem then states that any root in the fraction field is also in the base domain.

Titlerational root theorem
Canonical nameRationalRootTheorem
Date of creation2013-03-22 11:46:18
Last modified on2013-03-22 11:46:18
Ownerdrini (3)
Last modified bydrini (3)
Numerical id13
Authordrini (3)
Entry typeTheorem
Classificationmsc 12D10
Classificationmsc 12D05
Classificationmsc 26A99
Classificationmsc 26A24
Classificationmsc 26A09
Classificationmsc 26A06
Classificationmsc 26-01
Classificationmsc 11-00
Related topicFactorTheorem
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更新时间:2025/5/4 4:19:25