TY - JOUR
AU - Kostov, Vladimir
PY - 2024/08/14
Y2 - 2024/11/14
TI - On a problem inspired by Descartes' rule of signs
JF - Modern Mathematical Methods
JA - Modern Math. Methods
VL - 2
IS - 2
SE - Articles
DO -
UR - https://modernmathmeth.com/index.php/pub/article/view/38
SP - 103-116
AB - <p>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.</p>
ER -