Year: 2024
Type: article
Abstract: We study real univariate polynomials with non-zero coefficients and with all roots real, out of which exactly two positive. The sequence of coefficients of such a polynomial begins with \(m\) positive coefficients followed by \(n\) negative followed by \(q\) positive coefficients. We consider the sequence of moduli of their roots on the positive real half-axis; all moduli are supposed distinct. We mark in this sequence the positions of the moduli of the two positive roots. For \(m=n=2\), \(n=q=2\) and \(m=q=2\), we give the exhaustive answer to the question which the positions of the two moduli of positive roots can be.
Source: Modern Mathematical Methods
DOI: 10.64700/mmm.38
Author: Vladimir Kostov
Institution: Université Côte d'Azur
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413317955