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Question: Answered & Verified by Expert
If the cube roots of unity are $1, \omega, \omega^2$ then the roots of the equation $(x-1)^3+8=0$, are
MathematicsComplex NumberJEE MainJEE Main 2005
Options:
  • A
    $-1,-1+2 \omega,-1-2 \omega^2$
  • B
    $-1,-1,-1$
  • C
    $-1,1-2 \omega, 1-2 \omega^2$
  • D
    $-1,1+2 \omega, 1+2 \omega^2$
Solution:
1344 Upvotes Verified Answer
The correct answer is:
$-1,1-2 \omega, 1-2 \omega^2$
$(x-1)^3+8=0 \Rightarrow(x-1)=(-2)(1)^{1 / 3}$ $\Rightarrow x-1=-2$ or $-2 \omega$ or $-2 \omega^2$ or $n=-1$ or $1-2 \omega$ or $1-2 \omega^2$.

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