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arXiv · 1904.10694

Descartes' rule of signs and moduli of roots

Vladimir Petrov Kostov
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Abstract

A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For $c=1$ and $2$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?

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Vladimir Petrov Kostov. 2019-04-24. Descartes' rule of signs and moduli of roots. https://doi.org/10.5486/pmd.2020.8640

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