Only two co-efficient

Algebra Level 4

Let \(f(x)\) be a degree 6 monic polynomial having integer coefficients and positive zeroes, such that \(a_5=-12\) and \(a_0=64\), where \(a_i\) denotes the coefficient of \(x^{i}\).

Find \(f(1)+f(2)+f(3)\).

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