Let \(e_1\) and \(e_2\) be two distinct roots of the equation \(x^2-a x+2=0\). Let the sets \(\left\{a \in \mathbb{R}: e…

Let \(e_1\) and \(e_2\) be two distinct roots of the equation \(x^2-a x+2=0\). Let the sets \(\left\{a \in \mathbb{R}: e_1\right.\) and \(e_2\) are the eccentricities of hyperbolas\(\}=(\alpha, \beta)\), and \(\left\{a\in \mathbb{R}:e_1\right.\) and \(e_2\) are the eccentricities of an ellipse and a hyperbola, respectively\(\}=(\gamma, \infty)\). Then \(\alpha^2+\beta^2+\gamma^2\) is equal to:

[JEE Main 2026, 6 Apr (Shift 1)]