Q52.Let α = −1+i√32 . If a = (1 + α) ∑100k=0 α2k and b = ∑100k=0 α3k , then a and b, are the roots of the quadratic equation. (1) x2 + 101x + 100 = 0 (2) x2 −102x + 101 = 0 (3) x2 −101x + 100 = 0 (4) x2 + 102x + 101 = 0
What This Question Tests
The question requires using properties of cube roots of unity and the sum of a geometric progression to simplify expressions for 'a' and 'b', and then forming a quadratic equation from these roots.
Concepts Tested
Formulas Used
ω^3 = 1
1 + ω + ω^2 = 0
S_n = a(r^n - 1)/(r - 1)
x^2 - (sum of roots)x + (product of roots) = 0
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Cube roots of unity and Geometric Progression
- Year
- 2020
- Shift
- 08 Jan Shift 2
- Q Number
- Q52
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations, Class 11 Mathematics Ch 9: Sequences and Series
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