JEE Main 2026 Mathematics question
Let e₁ and e₂ be two distinct roots of the equation x²−ax+2=0. Let the sets {a∈ℝ : e₁ and e₂ are the eccentricities of hyperbolas} = (α, β), and {a∈ℝ : e₁ and e₂ are the eccentricities of an ellipse and a hyperbola, respectively} = (γ, ∞). Then α²+β²+γ² is equal to:
Answer: (C)
Solution
The roots are real and distinct when a²>8, and e₁e₂=2. Both eccentricities exceed 1 iff (e₁−1)(e₂−1)>0 and e₁+e₂>2, i.e.
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