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Proceedings of the American Mathematical Society

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Remarks on the Gauss-Lucas theorem in higher dimensional space


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 55 (1976), 97-102
MSC: Primary 30A08; Secondary 26A78
DOI: https://doi.org/10.1090/S0002-9939-1976-0435366-6
MathSciNet review: 0435366
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Abstract: A recent paper by J. B. Diaz and Dorothy Browne Shaffer extends the Gauss-Lucas Theorem to $ n$-dimensional Euclidean space. The authors leave open certain natural questions concerning the existence of ``zeros of the derivative". This paper answers three such questions, and suggests several other questions for further investigation.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0435366-6
Keywords: Polynomials, zeros of the derivative, Euclidean $ n$-space, gradient, Gauss-Lucas Theorem
Article copyright: © Copyright 1976 American Mathematical Society