2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174189First, we show that Sturm algorithm and Sylvester algorithm, which compute the number of real roots of a given univariate polynomial, lead to two dual tridiagonal determinantal representations of the polynomial. Next, we show that the number of real roots of a polynomial given by a tridiagonal determinantal representation is greater than the signature of this representation.Rings and Algebras12 - 15text