Vieta's Formulas for Quaternionic Polynomials

TL;DR

This paper extends Vieta's formulas to quaternionic polynomials, providing new relations and criteria for root sphericity, enhancing understanding of quaternion polynomial roots.

Contribution

It introduces quaternionic analogues of Vieta's formulas and establishes a criterion for the sphericity of polynomial roots.

Findings

Quaternionic Vieta's formulas derived

Criterion for root sphericity established

Enhanced understanding of quaternion polynomial roots

Abstract

The paper presents analogues of some Vieta formulas for quaternionic polynomials of the form $R_n(w)=\sum\limits_{m=0}^{n}A_mx^m$. A criterion for the sphericity of the root (zero) of a polynomial $R_n(w)$ is established.