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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