Computing the zeros of quaternion polynomials

A method is developed to compute the zeros of a quaternion polynomial with all terms of the form qkXk. This method is based essentially in Nivenʹs algorithm [1], which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematica 2.2 version are given.