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A new proof of Laguerre's theorem about the zeros of polynomials

Published online by Cambridge University Press:  17 April 2009

Abdul Aziz
Abdul Aziz
Affiliation:
Post Graduate Department of Mathematics, University of Kashmir, Hazratbal Srinagar – 190006KashmirIndia.
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Abstract

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An elementary new, simple and purely analytic proof of Laguerre's theorem about the zeros of the polar derivative of a polynomial P(z) with respect to the point α, is given. The proof is based on a lemma which is also of independent interest.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 131 - 138
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Grosswald, E., “Recent applications of some old work of Laguerre”, Amer. Math. Monthly, 86 (1979) 648–658.CrossRefGoogle Scholar
[2]Mardan, M., “Geometry of Polynomials”, second ed; Mathematical Surveys, No. 3, Amer. Math. Soc., New York 1966.Google Scholar
[3]Pólyá, G. and Szegö, G., Aufgaben und Lehrsatze aus der Analysis, Springer-Verlag, Heidelberg, New York, 1970).CrossRefGoogle Scholar