An algebra problem by Vicky Vignesh

Algebra Level 4

\[q(x) = x^2+ax+b, (a, b) \in \mathbb R\]

Find the number of real pairs \((a, b)\) such that whenever \(\alpha\) is a root of \(q(x)\) \(\alpha^2 -2\) is also a zero of \(q(x)\).

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