Exact Roots of Polynomials of Degree 20
Ex-Roots Of Equations Of Degree 20
Language: English - 219 pages
€23.58
Synopsis
For centuries, the equation has stood as the most perfect expression of mathematical truth—and yet one of its greatest challenges has persisted: the exact solution of high-degree polynomials. Since 1824, when Niels Henrik Abel declared that no general algebraic solution exists for equations of degree five or higher, this theorem has defined the limits of algebraic possibility.
But limits exist only until they are surpassed.
In Exact Roots of Polynomial Equations of Degree 20, I present the culmination of decades of research: a complete and exact symbolic solution for the 20th-degree polynomial equation. Built upon the profound structure of what is now known as Ezouidi’s Theorem, this achievement reveals that the boundaries erected by Abel’s impossibility are not absolute—they are historical misconceptions emerging from an incomplete mathematical framework.
About Mourad Sultan Ezouidi
The resolution of nth-degree polynomial equations has long been considered beyond the reach of classical algebraic methods. Traditional approaches, constrained by Abel’s theorem and the limitations of radicals, have failed to produce exact symbolic roots for equations of degree five and higher. For centuries, mathematicians have accepted this boundary as absolute — until the introduction of Ezouidi’s Theorem, a new and transformative approach to polynomial theory.
Ezouidi’s Theorem redefines how high-degree polynomial equations are understood and solved. By introducing a new structural framework that connects the coefficients of the polynomial through recursive relations and discriminant-based transformations, the theorem provides a path to derive exact symbolic roots without resorting to approximation or numerical iteration.
When applied to the nth-degree polynomial, Ezouidi’s Theorem unveils the underlying harmony between the coefficients and the recursively determined quantities . These relationships allow the equation to be systematically decomposed into solvable components, leading to closed-form expressions for the roots. This approach restores what was once thought impossible — a complete, algebraic, and exact solution to the nth-degree polynomial.
Through this method, each root of the equation emerges in its symbolic form, often expressed through radical and exponential relationships that maintain algebraic integrity. Unlike classical methods that rely on transformations or approximations, Ezouidi’s Theorem reveals the natural internal symmetry of the polynomial, demonstrating that the impossibility once asserted by Abel and Ruffini applies only to limited frameworks, not to all mathematical realities.
This chapter (or presentation) presents a detailed application of Ezouidi’s Theorem to nth-degree equations, showcasing step-by-step symbolic derivations, recursive coefficient analysis, and final expressions of the exact roots — a demonstration of how modern algebra evolves beyond its historical constraints.
The resolution of sixth-degree polynomial equations has long been considered beyond the reach of classical algebraic methods. Traditional approaches, constrained by Abel’s theorem and the limitations of radicals, have failed to produce exact symbolic roots for equations of degree five and higher. For centuries, mathematicians have accepted this boundary as absolute — until the introduction of Ezouidi’s Theorem, a new and transformative approach to polynomial theory.
Ezouidi’s Theorem redefines how high-degree polynomial equations are understood and solved. By introducing a new structural framework that connects the coefficients of the polynomial through recursive relations and discriminant-based transformations, the theorem provides a path to derive exact symbolic roots without resorting to approximation or numerical iteration.
When applied to the nth-degree polynomial, Ezouidi’s Theorem unveils the underlying harmony between the