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Question

If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?

A x^2 + 2x + 1 = 0 Correct Answer Incorrect Answer
B x^2 – 2x – 1 = 0 Correct Answer Incorrect Answer
C x^2 + 3x – 1 = 0 Correct Answer Incorrect Answer
D x^2 – 3x + 1 = 0 Correct Answer Incorrect Answer

Solution

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 Sum of the roots=-2 product=1 Required equation is x2 + 2x + 1 = 0

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