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JEE Main 2022 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2022

Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, , and f(1) = 1/3. If the equations f(x) = 0 and f∘f∘f∘f(x) = 0 have a common real root, then f(−3) is equal to

Answer: 25

Solution

Let , so and . Let the common root be , so and , i.e. f∘f∘f(0) = 0, so f∘f(p) = 0 and f(p) is a root of f, say (the other choice is symmetric). So $(p -

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Question ID VK-024735