For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.
Lucas's Root Theorem
See also
Gauss's Root Theorem, Jensen's Theorem, Lucas's TheoremExplore 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
Lucas's Root TheoremCite this as:
Weisstein, Eric W. "Lucas's Root Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LucassRootTheorem.html