The zeros of the derivative 
of a polynomial 
that are not multiple zeros of 
are the positions of equilibrium in the field of force
due to unit particles situated at the zeros of 
, where each particle repels with a force equal to the inverse
distance.
Gauss's Root Theorem
See also
Jensen's Theorem, Lucas's Root Theorem, Polynomial RootsExplore with Wolfram|Alpha
References
Walsh, J. L. "A Generalization of Jensen's Theorem on the Zeros of the Derivative of a Polynomial." Amer. Math. Monthly 62, 91-93, 1955.Referenced on Wolfram|Alpha
Gauss's Root TheoremCite this as:
Weisstein, Eric W. "Gauss's Root Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssRootTheorem.html