Squeezing Polynomial Roots a Nonuniform Distance

Abstract

Given a polynomial with all real roots, the Polynomial Root Squeezing Theorem states that moving two roots an equal distance toward each other, without passing other roots, will cause each critical point to move toward $(r_i + r_j)/2$, or remain fixed. In this note, we extend the Polynomial Root Squeezing Theorem to the case where two roots are squeezed together a nonuniform distance.