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Complex Numbers

If α, β are...

Question

If $α, β$ are the roots of $x^{2} + x + 1 = 0$ then $(\frac{α}{β} + \frac{β}{α})$ is equal to

A

- 1

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B

1

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C

2

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D

None

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Solution

The correct option is A $- 1$
From the given quadratice equation: $α + β = - 1$ and $α b e t a = 1$
$\frac{α}{β} + \frac{β}{α} = \frac{α^{2} + β^{2}}{α β} = \frac{(α + β)^{2} - 2 α β}{α β}$
$= \frac{(- 1)^{2} - 2 (1)}{1} = 1 - 2 = - 1$

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