On annuli containing all the zeros of a polynomial

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.