Villegas, Fernando Rodriguez2011-01-072011-01-072017-05-112011-01-072011-01-072017-05-112010-05May 2010http://hdl.handle.net/2152/ETD-UT-2010-05-998textWe study the quadratic form induced by the Bezoutian of two polynomials p and q, considering four problems. First, over R, in the separable case we count the number of configurations of real roots of p and q for which the Bezoutian has a fixed signature. Second, over Qp we develop a formula for the Hasse invariant of the Bezoutian. Third, we formulate a conjecture for the behavior of the Bezoutian in the non separable case, and offer a proof over R. We wrote a Pari code to test it over Qp and Q and found no counterexamples. Fourth, we state and prove a theorem that we hope will help prove the conjecture in the near future.application/pdfengBezoutianp-adicInterlacingHasse invariantthesis2011-01-07