Unified Inversion Method for Solving Polynomial Equations: A Reverse Detour to the Common Procedure

Thera are many solutions to polynomial equations that have been developed by mathematicians over the centuries. These methods adopt different approaches such as substitution, complex number algebra, trigonometry, reduction to depressed form, elimination and decomposition of the original polynomial into solvable products of polynomials of lesser degree. Historical preview of the methods is provided together with review of recent methods demonstrated for solving polynomial equations. This paper proposes a new unified method of solving polynomial equations based on the inversion of the nth roots to explicitly determine the root which is applicable to all polynomials within the limits of solvability of polynomials by radicals. The method follows a reverse route to the common methods and logically finds roots that are in a real number solution starting with complex numbers. By contrast, methods such as the Cardan’s solution to cubic equations give a solutions that have complex number parts whereas the roots are real numbers. The method is simple and intuitive to understand and use. Examples have been provided to demonstrate the application of the proposed method.