Some extensions of Eneström-Kakeya theorem (Q2785607)

In this paper some results concerning the location of zeros of polynomials in the complex plane are established. Among others it is proved the following theorem. If \(P(z)= a_nz^n+ a_{n-1} z^{n-1}+ \cdots +A_1z+a_0\) is a polynomial of degree \(n\) such that for some \(K\geq 1\), \(Ka_n \geq a_{n-1}\geq \cdots \geq a_2\geq a_1\geq a_0\), then all the zeros of \(P(z)\) lie in the disc \(|z+ (K-1) |\leq {Ka_n-a_0+ |a_0 |\over |a_n|}\). Some similar results which generalized the well known Eneström-Kakeya theorem, are also given.