On the location of zeros of a polynomial

Observing that for the zeros of polynomial p(z) = zn+ n−1 j=0 a jz j, Cauchy’s bound |z| < 1 + A, A = max 0≤ j≤n−1 |a j| does not reflect the fact that for A → 0, all zeros approach the origin z = 0, Boese and Luther suggested the proper bound |z| < R′,