Why it can't have 4 real roots ?!!

Algebra Level 3

\[(a-1)(x^{2}+x+1)^{2}-(a+1)(x^{4}+x^{2}+1)=0\] Provided that two roots of the above equation are real and distinct for \(a \in \mathbb{R}-A\). then find the set \(A\).

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