2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166994We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices, namely totally stable matrices and totally upper matrices.6 pagesClassical Analysis and ODEsCombinatorics26C10, 12D10, 30C15text