Zeros of a Two-parameter Family of Harmonic Quadrinomials

Abstract: In this paper, we determine the numb er of zeros and the zero inclusion regions of a two-parameter family of harmonic quadrinomials. We also determine a curve that separates sense-preserving and sense-reversing regions for these families of quadrinomials. Our work makes practical and effective use of the work of Wilmshurst, Khavinson, Dehmer, and also Bezouts theorem in the plane.