Closed-form solution of polynomial equations

TL;DR

This paper presents a novel method using the integral Cauchy theorem to derive explicit closed-form integral expressions for the roots of any degree univariate polynomial, providing a new analytical approach.

Contribution

It introduces a general closed-form integral solution for polynomial roots applicable to polynomials of any degree, expanding analytical tools in algebra.

Findings

Derived explicit integral formulas for polynomial roots

Applicable to polynomials of any degree

Provides a new analytical framework for solving polynomial equations

Abstract

Integral Cauchy theorem is used to derive closed-form expressions of the roots of a univariate polynomial of any degree as integrals of elementary functions.