Bezoutians

A Bezoutian is a mathematical tool used to analyze pairs of polynomials, especially in relation to their roots and common factors. It is represented as a special matrix constructed from the coefficients of two polynomials. The Bezoutian helps determine whether the polynomials share roots or have common factors and plays a key role in systems theory, control, and numerical analysis. Essentially, it provides a structured way to examine relationships between two equations, making it easier to study their solutions and properties in a rigorous, matrix-based framework.