Resultant

Summary

The resultant of two polynomials is a polynomial expression in their coefficients that, for nonzero leading coefficients, vanishes exactly when they have a common root. It is the determinant of the Sylvester matrix built from the coefficients. It lets one decide whether two polynomial equations have a common solution without solving them. The discriminant of $f$ is, up to a simple factor, the resultant of $f$ and its derivative.