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COMEDK2017MathematicsComplex Number

If the cube roots of unity are 1, , ² , then the roots of the equation (x-1)³+8=0 are

Options

  1. A-1,-1,-1
  2. B-1,-1+2 .-1-2 ²
  3. C-1,1+2 , 1+2 ²
  4. D-1,1-2 w i -2 w ²

Correct answer

D. -1,1-2 w i -2 w ²

Step-by-step solution

We have, aligned & &(x-1)³ &=-8=(-2)³ & & x-1 &=-2,-2 ,-2 ² & & x &=-1,1-2 , 1-2 ² aligned

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