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Common Roots

Roots of the ...

Question

Roots of the agebraic equation $x^{3} + x^{2} + x + 1 = 0$ are

(+ 1, + j, - 1)

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(+ 1, - 1, + 1)

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(0, 0, 0)

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(- 1, + 1, - j)

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Solution

The correct option is D $(- 1, + 1, - j)$
$x^{3} + x^{2} + x + 1 = 0$
$(x + 1) (x^{2} + j) = 0$
$\Rightarrow x = - 1, \pm j$

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