On Algebraic Solutions of Polynomial Equations of Degree n in one Variable

2006/05/07 by Gerry Martens, Martens, Gerry
Computer Science · #FOS: Mathematics #General Mathematics (math.GM) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0605183

openalex publication_date 2006/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will show that the roots of a polynomial equation in one variable of degree n are related to the solutions of a symmetric quadratic form in n-1 variables with constant positive integer coefficients. The classic polynomial notation will be rewritten to define a characteristic discriminant of a polynomial of degree n. A new set of characteristic roots allows expressing the characteristic discriminant as the result of a symmetric quadratic form.

Related

• Discriminants of Symmetric Polynomials
• The roots of any polynomial equation
• Solving polynomials with ordinary differential equations
• Some results on integer solutions of quadratic polynomials in two\n variables
• A short proof of solution formulas for the linear differential equations with constant coefficients