If α and β are the roots of equation x 2 – x + 1 = 0, then which equat
| If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?
A. x2 + 2x + 1 = 0
B. x2 – 2x – 1 = 0
C. x2 + 3x – 1 = 0
D. x2 – 3x + 1 = 0
Right Answer is: A
SOLUTION
Given, x2 – x + 1 = 0
Sum of roots = α + β = 1
Product of roots = αβ = 1 ⇒ β = 1/α
Thus, 
So, 
α3 + β3 = -2
Required
⇒ 
= 0
⇒ x2 + 2x + 1 = 0
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If α and β are the roots of equation x 2 – x + 1 = 0, then which equat