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Roots of an irreducible quartic

Source: Canada Repêchage 2014/5

June 18, 2016
algebrapolynomialirreducibility

Problem Statement

Let f(x)=x4+2x3−x−1f(x) = x^4 + 2x^3 - x - 1.
(a) Prove that f(x)f(x) cannot be written as the product of two non-constant polynomials with integer coefficients.
(b) Find the exact values of the 4 roots of f(x)f(x).
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