Bounds for the zeros of a quaternionic polynomial

In this paper, we obtain new bounds for the zeros of a quaternionic polynomial by implementing the maximum modulus theorem within the system of regular quaternionic setting. Using structural properties of zero sets adapted to the non-commutative setting, we derive explicit areas that contain all zeros of the polynomial. The obtained results extend and refine several known localization theorems for quaternionic polynomials. In particular, we generalize existing results concerning the location and distribution of zeros for quaternionic polynomials with real coefficients to a broader class.