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A refinement of the Gauss-Lucas theorem

Author: Dimitar K. Dimitrov
Journal: Proc. Amer. Math. Soc. 126 (1998), 2065-2070
MSC (1991): Primary 30C15, 26C10
MathSciNet review: 1452801
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Abstract: The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial $p$ lie in the convex hull $\Xi$ of the zeros of $p$. It is proved that, actually, a subdomain of $\Xi$ contains the critical points of $p$.

References [Enhancements On Off] (What's this?)

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  • 2. M. Marden, Geometry of Polynomials, Amer.Math.Soc.Surveys, no.3, Providence, R.I., 1966. MR 37:1562
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Additional Information

Dimitar K. Dimitrov
Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil

Keywords: Nontrivial critical point of a polynomial
Received by editor(s): December 29, 1996
Additional Notes: Research supported by the Brazilian foundation CNPq under Grant 300645/95-3 and the Bulgarian Science Foundation under Grant MM-414.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society