If α and β are the roots of the equation x2 - x + 1 = 0, then which equations will have roots α3 and β3?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. x2 + 2x + 1 = 0.
x2 - x + 1 = 0
αβ = 1
α + β = 1
Cubing on both sides
α3 + β3 + 3αβ (α + β) = 1
α3 + β3 + 3(1)(1) = 1
α3 + β3 = -2
α3 β3 = 1
Required equation = x2 + 2x + 1 = 0