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JEE Main Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main

The number of pairs of real numbers, such that whenever is a root of the equation , is also a root of this equation, is

Answer: (C)

Solution

The root set must be closed under . A double root needs , so or , giving and . Two distinct roots: (both fixed) gives ; a 2-cycle , gives

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Question ID VK-014299