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Gauss's Root Theorem


The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles situated at the zeros of P(z), where each particle repels with a force equal to the inverse distance.


See also

Jensen's Theorem, Lucas's Root Theorem, Polynomial Roots

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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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Gauss's Root Theorem

Cite this as:

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

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