Ezouidi's theorem and its proof

This document introduces a new method for solving polynomials using the discriminant formula developed by Mourad Sultan Ezouidi. The formula provides an exact, algebraic solution for polynomials of any degree, overcoming the limitations of traditional methods. It works by directly utilizing the polynomial's structure, determining both the nature of the roots (whether real, complex, or repeated) and their exact values. In contrast to traditional methods, which may approximate roots or fail for certain polynomials, the discriminant formula provides exact roots for all polynomial types, regardless of the degree or nature of the roots.The key advantage of this method lies in its ability to handle polynomials of higher degrees and those with repeated or complex roots, areas where traditional techniques struggle. Moreover, this approach has been applied to solve polynomials up to degree 18, further demonstrating its wide applicability. In addition to solving polynomials of degrees 3–10, a book containing detailed examples using this method has been published and adopted in European universities, which further demonstrates its value and effectiveness in solving complex polynomial equation