Solving 5th and 6th Degree Polynomial Equations Using Ezouidi’s Theorem
Ezouidi' Theorem
Language: English - 162 pages
€20.90
Synopsis
For centuries, mathematics has carried a deep paradox: while the equations of the universe can be written with perfect clarity, their exact solutions have often remained out of reach. Since 1824, when Niels Henrik Abel declared that no general formula in radicals exists for fifth-degree polynomial equations or higher, generations of mathematicians accepted this as an immutable law — a boundary that could never be crossed. But in this book, I prove that this limitation is not a law of nature, but a misunderstanding of algebraic structure itself.
In “Solving 5th and 6th Degree Polynomial Equations Using Ezouidi’s Theorem”, I present a complete, step-by-step symbolic method for determining the exact roots of fifth- and sixth-degree polynomial equations. This work forms a critical part of my lifelong research and stands as one of the central pillars of Ezouidi’s Theorem, a revolutionary approach that restores exact solvability to all polynomial degrees n.
The book begins with a historical and theoretical foundation, showing precisely why the classical methods — including Cardano’s, Ferrari’s, and Abel’s frameworks — fail to reach the truth.
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