New Six Solutions to Solve Sixth Degree Polynomial Equation in General Forms by Relying on Radical Expressions

TL;DR

This paper introduces six novel solutions for solving sixth degree polynomial equations using radical expressions, based on new theorems and reduction to quartic equations, enabling nearly simultaneous root calculation.

Contribution

The paper presents six new solutions for sixth degree polynomials derived from novel theorems, simplifying the solution process by reducing to quartic equations.

Findings

Six new solutions for sixth degree polynomials proposed.

Method enables nearly simultaneous calculation of roots.

Reduction to quartic equations simplifies the solution process.

Abstract

This paper presents new six solutions for sixth degree polynomial equation in general forms basing on new theorems, where the possibility to calculate the six roots of any sixth degree equation nearly simultaneously. The proposed roots for sixth degree polynomials in this paper are structured basing on new proposed solutions for quartic polynomial equations, which we developed in order to reduce the expression of any sixth degree polynomial to an expression of fourth degree polynomial.