Squares R.I.P

Algebra Level 3

Let \( f(x) \) be a cubic polynomial such that \( f(1) = 5, f(2) = 20, f(3) = 45 \).

Then find the product of roots of the equation below.

\[ \large [f(x)]^{2} + 3x \ f(x) + 2x^{2} = 0 \]

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