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JEE Main 2026 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2026

Consider the quadratic equation (n²−2n+2)x²−3x+(n²−2n+2)²=0, n∈ℝ. Let α be the minimum value of the product of its roots and β be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α and the common ratio is α/β, is:

Answer: (C)

Solution

Let A=n²−2n+2=(n−1)²+1≥1. Product of roots=A²/A=A, so α=1. Sum of roots=3/A,

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Question ID VK-015561