Prove that the equation
$$ z^3+wz+w=0 $$
admits three roots depending analytically on the parameter $w$, in the disk $|w-1|=1$.
I understand that the equation has three roots and these roots will depend on $w$. But I am not sure what it means to say "depending analytically on the parameter $w$, in the disk $|w-1|=1$."
Some guidance would be greatly appreciated.