Zeros of quaternion polynomials (Q5938908)

For each \(q \in \mathbb H\) let \([q]\) be the equivalence class of all elements \(q'\) having the form \(xqx^{-1}\) with some \(x \in \mathbb H\). Then the authors show that for a quaternionic polynomial of the form \(f(x) = (x - x_1)\dots (x - x_n)\) the subset \(\text{zero}(f) \cap [x_r]\) is nonempty for each \(r\). This leads to a computational method to determine the zeros of the polynomial.