Q61.Let a ∈R and let α, β be the roots of the equation x2 + 60 41 x + a = 0. If α4 + β4 = −30, then the product of all possible values of a is _____ .
What This Question Tests
This question requires applying Vieta's formulas and algebraic identities to find the sum of the fourth powers of the roots, then solving for the possible values of the coefficient 'a'.
Concepts Tested
Formulas Used
α + β = -b/a
αβ = c/a
α² + β² = (α+β)² - 2αβ
α⁴ + β⁴ = (α² + β²)² - 2(αβ)²
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📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of Quadratic Equations and Algebraic Identities
- Year
- 2023
- Shift
- 25 Jan Shift 2
- Q Number
- Q61
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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