On the Zeros of Polynomial With Real Coefficients
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Authors: M. I. MIR, J. BANOO, S. SARFARAJ AND J. G. DAR
DOI: 10.46793/KgJMat2606.1001M
Abstract:
The Eneström-Kakeya theorem provides essential bounds on the location of the zeros of a polynomial with positive coefficients. Lot of research work has been done regarding the classical theorem known as Eneström-Kakeya theorem concerning the regions containing zeros of a polynomial. This theorem states that if F(z) = ∑ λ=0nfλzλ is a polynomial with degree n with real coefficients satisfying 0 ≤ f0 ≤ f1 ≤ f2 ≤
≤ fn, then all the zeros of F(z) lie in |z|≤ 1. In this article,
we prove several extensions of this theorem which impose restrictions only on the
coefficients f0,f1,…,fn−1 and leaves the coefficient fn to vary freely over the whole
complex plane.
Keywords:
Complex polynomials, location of zeros, Eneström–Kakeya theorem, m onotonicity.
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