# 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 x

^{2}– x + 1 = 0, then which equation will have roots α^{3}and β^{3}?A. x^{2} + 2x + 1 = 0

B. x^{2} – 2x – 1 = 0

C. x^{2} + 3x – 1 = 0

D. x^{2} – 3x + 1 = 0

### Right Answer is: A

#### SOLUTION

Given, x^{2} – x + 1 = 0

Sum of roots = α + β = 1

Product of roots = αβ = 1 ⇒ β = 1/α

Thus,

So,

α^{3} + β^{3} = -2

Required

⇒ = 0

⇒ x^{2} + 2x + 1 = 0

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If α and β are the roots of equation x 2 – x + 1 = 0, then which equat