Test SeriesFree PYQsExamsPricing

JEE Main 2024 Mathematics question

MathematicsQuadratic Equations and InequalitiesJEE Main 2024

Let α, β be the roots of the equation x² – x + 2 = 0 with Im(α) > Im(β). Then α⁶ + α⁴ + β⁴ – 5α² is equal to .

Answer: 13

Solution

x² = x − 2 gives x⁴ = −4 − 3x² (from (x² + 2)² = x² ⇒ x⁴ + 4 + 4x² = x²) and x⁶ = 12 + 5x². So α⁶ − 5α² = 12. Also α⁴

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-016916