Bôcher's Theorem

The finite zeros of the derivative  of a nonconstant rational function  that are not multiple zeros of  are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of  and particles of negative mass at the poles of , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.

REFERENCES:

Bôcher. "The Location of Critical Points." Amer. Math. Soc. Colloq. Publ. 34, 1950.

Walsh, J. L. "A New Generalization of Jensen's Theorem on the Zeros of the Derivative of a Polynomial." Amer. Math. Monthly68, 978-983, 1961.