Exact Solutions of Polynomial Equations from Degree 1 to 20
An Application of Ezouidi’s Theorem to General Algebraic Equations
Language: English - 371 pages
€30.72
Synopsis
For centuries, the exact resolution of polynomial equations has been a central problem in algebra. While equations of low degree were solved in closed form, higher-degree equations were long believed to resist general exact methods, a belief reinforced by Abel’s theorem and classical Galois theory.
This book introduces a systematic and exact approach to solving polynomial equations of degrees 1 through 20, grounded in Ezouidi’s Theorem (EMST). The method does not depend on radicals or special symmetries. Instead, it constructs derived polynomials whose roots encode the complete solution of the original equation. Through this transformation, even high-degree equations are reduced to algebraically structured systems that admit exact determination of roots.
The work treats general polynomials, including those with multiple roots and arbitrary multiplicities, and provides explicit constructions, proofs, and illustrative examples for each degree. The progression from low to higher degrees is logical and cumulative, making the method transparent and verifiable.
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