On the Zeros of the Polar Derivative of a Polynomial

Document Type: Original Article


Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India


Let P(z) be a polynomial of degree n whose coefficients satisfy an ≥ an−1 ≥ ... ≥ a0 > 0.Then according to the Enstrom-Kakeya Theorem, all the zeros of P(z) lie in |z|≤ 1. Aziz and Mohammad have shown that under the same condition on coeffients the zeros of P(z) whose modulus is greater than or equal to n/(n+1) are simple. In this paper, we extend the above result to the polar derivative.


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