A method to determine whether two polynomials are relatively prime

In this paper, it is established that a necessary and sufficient condition for two monic polynomialsf(lambda)andg(lambda)to have a common root is thatdet [f(B)] = 0ordet [g(A)] = 0, whereAandBare, respectively, the companion matrices associated withf(lambda)andg(lambda). The simplicity of this method is illustrated by examples.