Let $a,b,c,d$ be the roots of $x^4+x^2+1=0$. Then the equation whose roots are $a^2,b^2,c^2,d^2$ are-

If a is a root of x^4 + x^2 + 1 = 0, then squaring this relation gives a^4 = -a^2 - 1. We need the new equation to have roots y = a^2, so we rewrite the relation in terms of y as y^2 = -y - 1, or y^2 + y + 1 = 0. Because squaring a root results in one of two complex roots satisfying this quadratic, the polynomial with roots a^2, b^2, c^2, and d^2 is the square of this quadratic factor. The required equation is (x^2 + x + 1 = 0)^2.

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