Zeros of quaternion polynomials Original Research Article

It is well known that, over a division ring, every zero of a polynomial f(x) = (x − x1)…(x − xn) is congruent to xr for some r. In this note, we show further that, over the quaternion field, there exists at least one quaternion qr congruent to each xr, and that, through this result, a constructive method for determining the zeros of quaternion polynomials can be established.