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.
Bôcher's Theorem
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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. Monthly 68, 978-983, 1961.Referenced on Wolfram|Alpha
Bôcher's TheoremCite this as:
Weisstein, Eric W. "Bôcher's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BochersTheorem.html