# Minimal polynomial

Number Theory Level 5

Let $$\alpha = \sqrt{5}-\sqrt{3}$$, and let $$f(x)$$ be the minimal polynomial of $$\alpha$$. That is, $$f(x)$$ is a monic polynomial with rational coefficients of the smallest possible nonzero degree such that $$f(\alpha) = 0$$.

Find $$f(1)$$.

×