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JEE Main 2024 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2024

Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that ax² + bx + c = 0 has all real roots is m/n, gcd(m, n) = 1, then m + n is equal to ........

Answer: 19

Solution

Real roots need b² ≥ 4ac. For b = 1: none. For b = 2: ac ≤ 1, so (1, 1): 1 case. For b = 3: ac ≤ 9/4, so (1,1), (1,2), (2,1): 3 cases. For b = 4: ac ≤ 4,

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Question ID VK-016555