Homotopy function is used in conjunction with homotopy continuation methods (HCM) and a classical numerical method to approximate the roots of nonlinear algebraic equations, particularly in solving polynomial equations. In this paper, we develop a new function, known as quadratic parameter homotopy function, and apply it to solve several non- application equations and several application equations. This homotopy function is used in two homotopy methods i.e., Newton-HCM and Ostrowski-HCM. The results obtained indicate that the proposed homotopy function performs better than the existing homotopy functions.
