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JEE Main 2024 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2024

Let x₁, x₂, x₃, x₄ be the solution of the equation 4x⁴ + 8x³ − 17x² − 12x + 9 = 0 and (4 + x₁²)(4 + x₂²)(4 + x₃²)(4 + x₄²) = m. Then the value of m is .

Answer: 221

Solution

With P(z) = 4z⁴ + 8z³ − 17z² − 12z + 9 = 4∏(z − xᵢ): ∏(4 + xᵢ²) = ∏(xᵢ − 2i)(xᵢ + 2i) =

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Question ID VK-011751