JEE Main 2024 Mathematics question

Let α, β be the roots of the equation x² + 2√2x − 1 = 0. The quadratic equation, whose roots are α⁴ + β⁴ and (1/10)(α⁶ + β⁶), is

Answer: (C)

Solution

α + β = −2√2 and αβ = −1, so α² + β² = 8 + 2 = 10. α⁴ + β⁴ = 10² − 2 = 98. α⁶ + β⁶ = (α² + β²)³ − 3(αβ)²(α²

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Question ID VK-016553