Let $\displaystyle f(z)=\sum_{n=0}^{\infty} a_n z^n $ be analytic at {z: |z|<R} and satisfies:

$\displaystyle |f(z)| \leq M $ for every |z|<R.

Let's define: d=the distance between the origin and the closest zero of f(z).

Prove: $\displaystyle d \geq \frac{R|a_0|}{M+|a_0|}$.

Hope you'll be able to help me

Thanks !