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Lucas's Root Theorem


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.


See also

Gauss's Root Theorem, Jensen's Theorem, Lucas's Theorem

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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.

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Lucas's Root Theorem

Cite this as:

Weisstein, Eric W. "Lucas's Root Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LucassRootTheorem.html

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