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On the location of critical points of polynomials
Published online by Cambridge University Press: 09 April 2009
Abstract
Let all the zeros of a polynomial P(z) of degree n lie in |z|≤ 1 and a be a given complex number. In this paper we study the location of the zeros of higher derivatives of the polynomial (z – z) P(z) and obtain certain generalizations of some results of Rahman and Rubinstein. We shall also extend a result of Goodman, Rahman and Ratti for the zeros of the polar derivative of the polynomial P(z) given P(l) = 0.
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- Copyright © Australian Mathematical Society 1984
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