Let \(f(x)=3\sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum …

Let \(f(x)=3\sqrt{x-2}+\sqrt{4-x}\) be a real valued function. If \(\alpha\) and \(\beta\) are respectively the minimum and the maximum values of \(f\), then \({\alpha }^{2}+2{\beta }^{2}\) is equal to

[JEE Main 2024, 4 Apr (Shift 2)]