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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