Real Univariate Quintics

TL;DR

This paper derives simple polynomial conditions from the Sturm sequence to determine the real and complex root multiplicities and order of roots for general monic real quintic polynomials.

Contribution

It provides a straightforward method to analyze root multiplicities and order for real quintic polynomials using Sturm sequences.

Findings

Polynomial conditions for root multiplicities are explicitly derived.

Method simplifies the analysis of real roots in quintic equations.

Provides a systematic approach for root classification.

Abstract

For the general monic quintic with real coefficients, polynomial conditions on the coefficients are derived as directly and as simply as possible from the Sturm sequence that will determine the real and complex root multiplicities together with the order of the real roots with respect to multiplicity.