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.