# Minimum Monic

Algebra Level 5

$$f(x)$$ is a monic quadratic polynomial with positive real roots, and satisfies $$f(1) = 441$$. What is the minimum value of $$f(0)$$?

Details and assumptions

A monic polynomial has a leading coefficient of 1, i.e. $$f(x) =x^n + \ldots$$ for some non-negative integer $$n$$.

The roots of the polynomial may be repeated real roots.

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