# Smallest polynomial with given roots

Algebra Level 3

Let $$f(x)$$ be a monic polynomial with real coefficients such that $$2$$ and $$1+i$$ are both roots of $$f.$$ Suppose that $$f$$ has the smallest possible degree given these requirements. What is $$f(3)?$$

Clarification: $$i=\sqrt{-1}$$.

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