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We prove that the author's powersum formula yields anonzero expression for a particular linear ordinary differentialequation, called a resolvent, associated with aunivariate polynomial whose coefficients lie in a differentialfield of characteristic zero provided the distinct roots of thepolynomial are differentially independent over constants. Bydefinition, the terms of a resolvent lie in the differential fieldgenerated by the coefficients of the polynomial, and each of theroots of the polynomial are solutions of the resolvent. Oneexample shows how the powersum formula works. Another exampleshows how the proof that the formula is not zero works

Powersum formula for polynomials whose distinct roots are differentially independent over constants