Q61.If α and β are the roots of the equation x2 −x + 1 = 0, then α2009 + β2009 = (1) −1 (2) 1 (3) 2 (4) −2
What This Question Tests
This question requires recognizing the roots of the given quadratic equation as related to the cube roots of unity and then applying properties of ω to simplify the power expression.
Concepts Tested
Formulas Used
x^2 - x + 1 = 0 roots are -ω, -ω^2
ω^3 = 1
1 + ω + ω^2 = 0
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Roots of unity
- Year
- 2010
- Shift
- Unknown
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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