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)=a0+a1z+a2z2+⋯+anznp(z)=a0+a1z+a2z2+⋯+anzn, where aiai’s are complex coefficients and zz 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.