Using the Roots of a Polynomial

Calculus Level 4

What is the smallest degree of a non-constant complex polynomial \(f(x)\), such that the only roots of \(f\) are \(0\), \(2\) and \(3\), and the derivative of \(f(x)\) is divisible by \(8x^2-24x+7\)?

Details and assumptions

All roots of \(f(x)\), real or complex, are in the set \(\{0,2,3\}\).

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