Bézout matrix

A Bézout matrix is a mathematical tool used to analyze two polynomials, particularly in relation to their common roots. It’s constructed from the coefficients of the polynomials and helps determine whether they share any roots, as well as details about those roots. Specifically, if the Bézout matrix is singular (has a determinant of zero), the polynomials share at least one root. This matrix plays a key role in algebra and polynomial theory, aiding in solving problems related to polynomial equations and their intersections without explicitly finding the roots themselves.