The number of pairs \((a, b)\) of real numbers, such that whenever \(\alpha\) is a root of the equation \(x^2+a x+b=0\),…

The number of pairs \((a, b)\) of real numbers, such that whenever \(\alpha\) is a root of the equation \(x^2+a x+b=0\), \(\alpha^2-2\) is also a root of this equation, is:

[JEE Main 2021, 1 Sep (Shift 2)]