Let \( e_{1} \) and \( e_{2} \) be two distinct roots of the equation \( x^{2}-ax+2=0 \). Let the sets \( \{\, a \in \mathbb{R} : e_{1} \) and \( e_{2} \) are the eccentricities of hyperbolas \} \( = (\alpha,\beta) \), and \( \{\, a \in \mathbb{R} : e_{1} \) 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:
