# 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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