JEE Main 2024 Mathematics question
Let α and β be the roots the equation px² + qx − r = 0, where p ≠ 0. If p, q and r be the consecutive terms of a non-constant G.P. and , then the value of (α − β)² is:
Answer: (A)
Solution
With common ratio ρ, q = pρ and r = pρ²: 1/α + 1/β = q/r = 1/ρ = 3/4. Then (α − β)² = q²/p² + 4r/p = 5ρ² = 80/9.