Document Type

Article

Publication Date

2004

Abstract

The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of p' lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of p.

Publication Title

Proceedings of the American Mathematical Society

Volume

132

Issue

10

First Page

2973

Last Page

2981

Required Publisher's Statement

First published in "Proceedings of the American Mathematical Society" in 2004, published by the American Mathematical Society.

Included in

Mathematics Commons

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