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 polynomials
f(\lambda)
and
g(\lambda)
to have a common root is that
\det [f(B)] = 0
or
\det [g(A)] = 0
, where
A
and
B
are, respectively, the companion matrices associated with
f(\lambda)
and
g(\lambda)
. The simplicity of this method is illustrated by examples.