The 8th-Degree Equation Solved Exactly

Despite this limitation, the study of polynomial equations did not end. Modern algebra has shown that impossibility results concern methods, not the intrinsic existence or structure of roots. This distinction motivates the search for alternative frameworks capable of describing and reconstructing roots without reliance on radicals or classical factorization techniques. In this work, we introduce Ezouidi’s Theorem, a new invariant-based approach to polynomial equations of arbitrary degree. The theorem associates to a given polynomial a relative polynomial of the same degree and provides an explicit reconstruction formula that recovers the roots of the original equation from algebraic invariants. The method is purely algebraic, degree-independent, and does not depend on radical expressions