let $ B(0,1) = \{ z\in \mathbb{C} | |z|<1\} $ and $ f $ be an holomorphic function on $ B(0,1) $ such that $ f(z)\in\mathbb{R} \iff z\in\mathbb{R} $
Prove: $ f $ has at most 1 root in $ B(0,1) $
i think this exercise requires rouche theorem or the argument principle theorem but i cant see how to use it