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Vol. 49 No. 4 (2023)
Serdica Mathematical Journal

Articles

On Descartes' rule of signs for hyperbolic polynomials

https://doi.org/10.55630/serdica.2023.49.251-268

Published 21-12-2023

  • Vladimir Petrov Kostov

Vladimir Petrov Kostov
Université Côte d'Azur

Abstract

We consider univariate real polynomials with all real roots and with two sign changes in the sequence of their coefficients which are all non-vanishing. Assume that one of the changes is between the linear and the constant term. By Descartes' rule of signs, such degree \(d\) polynomials have 2 positive and \(d-2\) negative roots. We consider the possible sequences of the moduli of their roots on the real positive half-axis. When these moduli are distinct, we give the exhaustive answer to the question which positions can the moduli of the two positive roots occupy.

2020 Mathematics Subject Classification:

26C10

Keywords

real polynomial in one variable, hyperbolic polynomial, sign pattern, Descartes' rule of signs

Full text

Author Details

Vladimir Petrov Kostov

Université Côte d'Azur
Laboratoire de Mathématiques “Jean Alexandre Dieudonné”
06108 Nice, France
e-mail: vladimir.kostov@unice.fr

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