Reciprocating the Roots of a Quintic

Algebra Level 5

Let f(x)=5x5+3x42x311x2+3x5, f(x)=5x^5 + 3x^4 - 2x^3 - 11x^2 + 3x - 5 , and let g(x)g(x) be the polynomial such that there is a bijection between the roots of g(x) g(x) and the reciprocals of the roots of f(x) f(x) , and the gcd of the coefficients of g(x)g(x) is 1. Find g(3)|g(3)|.


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

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