In this paper, it is established that a necessary and sufficient condition for two monic polynomialsf(λ)andg(λ)to have a common root is that [f(B)] = 0or [g(A)] = 0, whereAandBare, respectively, the companion matrices associated withf(λ)andg(λ). The simplicity of this method is illustrated by examples.
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Vogt et al. (1970) studied this question.