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On the zeros of a polynomial and its derivative

Published online by Cambridge University Press:  17 April 2009

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

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Let P(z) be a polynomial of degree n and P′(z) be its derivative. Given a zero of P′(z), we shall determine regions which contains at least one zero of P(z). In particular, it will be shown that if all the zeros of P(z) lie in |z| < 1 and W1, W2, …, Wn−1 are the zeros of P′(z), then each of the disks |(z/2)–wj| < ½ and |z–Wj| < 1, j = 1, 2, …, n−1 contains at least one zero of P(z). We shall also determine regions which contain at least one zero of the polynomials mP(z) + zP′(z) and P′(z) under some appropriate assumptions. Finally some other results of similar nature will be obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 245 - 255
Copyright
Copyright © Australian Mathematical Society 1985

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