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JEE Main 2026 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2026

Let α, β be the roots of the equation x² − 3x + r = 0 and , 2β be the roots of the equation x² + 3x + r = 0. If the roots of the equation x² + 6x = m are 2α + β + 2r and α − 2β − , then m is equal to:

Answer: (D)

Solution

α + β = 3 and α/2 + 2β = −3 give α = 6, β = −3, so r = αβ = −18. Then 2α + β + 2r = 12 − 3 − 36 = −27 and α −

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Question ID VK-015110