On the Zeros of $R$-Bonacci Polynomials and Their Derivatives

TL;DR

This paper investigates the zeros of $R$-Bonacci polynomials and their derivatives, confirming a conjecture in specific cases and deriving explicit formulas for roots in certain scenarios.

Contribution

It provides new insights into the zeros of $R$-Bonacci polynomials, including proofs of conjectures and explicit root formulas for derivatives in special cases.

Findings

Confirmed a conjecture about zeros for some cases

Derived explicit formulas for roots of derivatives

Analyzed zeros of $R$-Bonacci polynomials

Abstract

The purpose of the present paper is to examine the zeros of $R$-Bonacci polynomials and their derivatives. We confirm a conjecture about the zeros of $R$-Bonacci polynomials for some special cases. We also find explicit formulas of the roots of derivatives of $R$-Bonacci polynomials in some special cases.