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Consider \( e_1 \) and \( e_2 \) be roots of the equation \( x^2 - a x + 2 = 0 \). Set of exhaustive values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricities of hyperbolas then \( a \in [\alpha, \beta) \) and set of values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricity of the parabola and ellipse is \( (\gamma, \infty) \) then \( (\alpha^2 + \beta^2 + \gamma^2) \) equal:
Consider \( e_1 \) and \( e_2 \) be roots of the equation \( x^2 - a x + 2 = 0 \). Set of exhaustive values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricities of hyperbolas then \( a \in [\alpha, \beta) \) and set of values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricity of the parabola and ellipse is \( (\gamma, \infty) \) then \( (\alpha^2 + \beta^2 + \gamma^2) \) equal:
Updated On: Apr 6, 2026
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Correct Answer: 25
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