Let $\displaystyle f(z)$ be analytic in the disk $\displaystyle |z| <1$. If $\displaystyle f(z)$ has a zero of order 2 at the origin and $\displaystyle |f(z)| \le 1$ in that disk. Prove that $\displaystyle |f(z)|\le|z|^2$ in $\displaystyle |z|<1$

I have no idea where to start. Thank you.