Reciprocating the Roots of a Quintic

Algebra Level 5

Let \( f(x)=5x^5 + 3x^4 - 2x^3 - 11x^2 + 3x - 5 ,\) and let \(g(x) \) be the polynomial such that there is a bijection between the roots of \( g(x) \) and the reciprocals of the roots of \( f(x) \), and the gcd of the coefficients of \(g(x) \) is 1. Find \(|g(3)|\).


Notice the relationship between \(g(x)\) and \(f(x)\) concerning coefficients.

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