Abstract: In this research, the sets of spherical roots, real roots, isolated complex roots, pure imaginary quaternion roots and roots in R + R+ Rj and R + R+ Rk of a quaternion polynomial Q(t) are determined by corresponding these sets to the sets of real or complex roots of some real or complex polynomials determined by Q(t). Thus, the counting and classifying methods for such polynomials can be used for the counting and classifying of the aforementioned roots of quaternion polynomials.

Key words: quaternion, polynomial, spherical root, isolated root, complex root