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Abstract: For a polynomial p(z) = anQn
t=1(z − zt) of degree n having all its zeros in |z| ≤ K, K ≥ 1 it is known that
max
|z|=1|p0(z)| ≥ 2 1 + Kn
( n X
t=1
K K + |zt|
) max
|z|=1|p(z)| .
By assuming a possible zero of order m, 0 ≤ m ≤ n − 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.
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