rational root theorem

Consider the polynomialPlanetmathPlanetmath


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.

Title rational root theorem
Canonical name RationalRootTheorem
Date of creation 2013-03-22 11:46:18
Last modified on 2013-03-22 11:46:18
Owner drini (3)
Last modified by drini (3)
Numerical id 13
Author drini (3)
Entry type Theorem
Classification msc 12D10
Classification msc 12D05
Classification msc 26A99
Classification msc 26A24
Classification msc 26A09
Classification msc 26A06
Classification msc 26-01
Classification msc 11-00
Related topic FactorTheorem