Original scientific paper

Degree 6 Hyperbolic Polynomials and Orders of Moduli

Yousra Gati orcid.org/0000-0003-3943-1898 ; University of Carthage, La Marsa, Tunisia
Vladimir Petrov Kostov ; Universite Cote d’Azur, Parc Valrose, France
Mohamed Chaouki Tarchi ; University of Carthage, La Marsa, Tunisia

Abstract

We consider real univariate degree d real-rooted polynomials with non-vanishing coefficients. Descartes’ rule of signs implies that such a polynomial has ˜c positive and ˜p negative roots counted with multiplicity, where ˜c and ˜p are the numbers of sign changes and sign preservations in the sequence of its coefficients, ˜c + ˜p = d. For d = 6, we give the exhaustive answer to the question: When the moduli of all 6 roots are distinct and arranged on the real positive half-axis, in which positions can the moduli of the negative roots be depending on the signs of the coefficients?

Keywords

real polynomial in one variable; hyperbolic polynomial; sign pattern; Descartes’ rule of signs

Hrčak ID:

321245

URI

https://hrcak.srce.hr/321245

Publication date:

7.10.2024.

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