Minimum Monic

Algebra Level 5

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

Details and assumptions

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

The roots of the polynomial may be repeated real roots.

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