Document Type
Article
Publication Date
2004
Keywords
roots of polynomials, critical points of polynomials, Gauss-Lucas theorem
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.
Recommended Citation
Ćurgus, Branko, "A Contraction of the Lucas Polygon" (2004). Mathematics Faculty Publications. 6.
https://cedar.wwu.edu/math_facpubs/6
Subjects - Topical (LCSH)
Polynomials
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
