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JEE Main 2022 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2022

Let a, b be two non-zero real numbers. If p and r are the roots of the equation and q and s are the roots of the equation , such that 1/p, 1/q, 1/r, 1/s are in A.P., then is equal to .

Answer: 38

Solution

p + r = 8a, pr = 2a, q + s = −12b and qs = 6b. So 1/p + 1/r = (p + r)/(pr) = 4 and 1/q + 1/s = (q + s)/(qs) = −2. Since 1/p, 1/q, 1/r, 1/s are in A.P., 1/p + 1/r = 2/q and 1/q + 1/s = 2/r. So 2/q = 4

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Question ID VK-024827