On a problem inspired by Descartes' rule of signs
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.
Authors
- Vladimir Petrov Kostov (ORCID: https://orcid.org/0000-0001-5836-2678)
Institutions
- Université Côte d'Azur (FR)
- Observatoire de la Côte d’Azur (FR)
Publication Details
- Journal
- Modern Mathematical Methods
- Published
- 2024-08-14
- DOI
- https://doi.org/10.64700/mmm.38
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00