  The polynomials with quaternion coefficients have two kind of roots: isolated
and spherical. A spherical root generates a class of roots which contains only
one complex number $z$ and its conjugate $\bar{z}$, and this class can be
determined by $z$. In this paper, we deal with the complex roots of quaternion
polynomials. More precisely, using B\'{e}zout matrices, we give necessary and
sufficient conditions, for a quaternion polynomial to have a complex root, a
spherical root, and a complex isolated root. Moreover, we compute a bound for
the size of the roots of a quaternion polynomial.
