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JEE Main 2024 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2024

Let S = {sin²2θ : (sin⁴θ + cos⁴θ)x² + (sin 2θ)x + (sin⁶θ + cos⁶θ) = 0 has real roots}. If α and β be the smallest and largest elements of the set S, respectively, then 3((α − 2)² + (β − 1)²) equals…..

Answer: 4

Solution

With s = sin²2θ: sin⁴θ + cos⁴θ = 1 − s/2 and sin⁶θ + cos⁶θ = 1 − 3s/4. The discriminant s − 4(1 − s/2)(1

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Question ID VK-011388