Annular Bounds for the Zeros of a Polynomial. (original) (raw)

Bounds for the zeros of a polynomial

International Journal of Recent Scientific Research

In this paper we find a bound for all the zeros of a polynomial in terms of its coefficients similar to the bound given by Cauchy's classical theorem.

Bounds for the Zeros of Polynomials

2013

In this paper we find bounds for the zeros of a class of polynomials whose coefficients or their real and imaginary parts are restricted to certain conditions. Our results improve and generalize many known results in this direction.

On the location of the zeros of certain 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).

On annuli containing all the zeros of a polynomial

Mathematical and Computer Modelling, 2010

In this paper, we obtain the annuli that contain all the zeros of the polynomial p(z) = a 0 + a 1 z + a 2 z 2 + • • • + a n z n , where a i 's are complex coefficients and z is a complex variable. Our results sharpen some of the recently obtained results in this direction. Also, we develop a MATLAB code to show that for some polynomials the bounds obtained by our results are considerably sharper than the bounds obtainable from the known results.

Note on the location of zeros of polynomials

2011

In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.

Zero Bounds for a Certain Class of Polynomials

In this paper we give a bound for the zeros of a polynomial with complex coefficients. Our results generalize some known results in addition to giving a way for some new results. Mathematics Subject Classification: 30 C 10, 30 C 15

On the zeros of a polynomial

2015

In this paper we consider the problem of finding the number of zeros of a polynomial in a prescribed region by subjecting the real and imaginary parts of its coefficients to certain restrictions.