# 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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