, Bôcher's theorem
, named after Maxime Bôcher
, states that the finite zeros
of the derivative
of a nonconstant rational function
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
and particles of negative mass at the poles
, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.