Bôcher's theorem

In mathematics, Bôcher's theorem, named after Maxime Bôcher, states that the finite zeros of the derivative $r\text{'}(z)$ of a nonconstant rational function $r(z)$ that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of $r(z)$ and particles of negative mass at the poles of $r(z)$, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.