# Minimal Polynomial

Algebra Level 5

Let $$\alpha = i-\sqrt{2}$$, where $$i = \sqrt{-1}$$, and $$f(x)$$ be the minimal polynomial of $$\alpha$$. That is, $$f(x)$$ is a monic polynomial with rational coefficients of smallest possible nonzero degree such that $$f(\alpha) = 0$$.

Find $$f(1)$$.

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