Squares R.I.P

Algebra Level 3

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

Then find the product of roots of the equation below.

[f(x)]2+3x f(x)+2x2=0 \large [f(x)]^{2} + 3x \ f(x) + 2x^{2} = 0

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