On the zeros of R-Bonacci polynomials and their derivatives

2012

In this paper, we establish some relations between the zeros and coefficients of a polynomial and thereby prove a few results concerning stable polynomials.

Alsrmcr -We study some fundamental properties of generalized Fibonacci polynomials, by using the properties and characteristics of classical Fibonacci polynomials as a motivation. We derive the generating function and an explicit representation of these polynomials. A trace relation for a related r x r matrix Q. is derived. We then

Comptes Rendus. Mathématique, 2021

In this paper, we use particular polynomials to establish some results on the real rootedness of polynomials. The considered polynomials are Bell polynomials and Hermite polynomials.

Publications de l'Institut Math?matique (Belgrade)

We extend Aziz and Mohammad's result that the zeros, of a polynomial P (z) = n j=0 a j z j , ta j a j−1 > 0, j = 2, 3,. .. , n for certain t (> 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae iα | < a/(2n); a > 0, max |z|=a |P (z)| = |P (ae iα)|, for r < a < 2, r being the greatest positive root of the equation x n − 2x n−1 + 1 = 0, and finally obtained an upper bound, for moduli of all zeros of a polynomial, (better, in many cases, than those obtainable from many other known results).

In this paper we locate the regions containing all or some of the zeros of a certain class of polynomials subjected to certain coefficient conditions.

2018

In this paper we define two new classes of polynomials associated with generalized Fibonacci polynomials. We call them h(x)-B-q-bonacci polynomials and incomplete h(x)-B-q-bonacci polynomials. We present some identities for the two classes of polynomials, and the convolution property of h(x)-B-q-bonacci polynomials and its applications.

1998

Let P(z) be a polynomial of degree n with real or complex coefficients, In this paper we obtain a ring shaped region containing all the zeros of P( z), Our results include, as special cases, several known extensions of Enestrom-Kakeya theorem on the zeros of a polynomiaL We shall also obtain zero free regions for certain class of analytic functions. n THEOREMB. LetP(z) = L aki ¥=-°be apolynomial with complex coefficients k=O such that I arg ak -131 :::; a :::;~, k = 0, l, ... , n for some 13, and Mathematics subject classification (1991): 30CIO,30CI5.

Scientific Letters of University of Rzeszow Technology - Mechanics

In this paper, we present some interesting results concerning the location of zeros of Lacunary-type of polynomial in the complex plane. By relaxing the hypothesis and putting less restrictive conditions on the coefficients of the polynomial, our results generalize and refines some classical results.

Journal of The London Mathematical Society-second Series, 1983

We show here, among other results, that there exist two monic polynomials P,Q with integral coefficients which have the same set of complex roots and are such that their derivatives also have the same roots, but there are no positive integers m, n such that P m = Q".

Annales UMCS, Mathematica, 2011

For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.