If cube roots of unity are 1,w,w2 then roots of the equation (x-1)3+8=0 are
-1,-1,-1
-1,-1+2w,-1-2w2
-1,1-2w,1-2w2
-1,1-2w,-1-2w2
Finding the roots of the equation:
Given, (x-1)3+8=0
⇒ (x-1)3=-8
⇒ (x-1)=(-8)1/3
⇒ x-1=81/3(-1)1/3
⇒ x-1=2(-1,-w,-w2)
⇒ x=1+2(-1,-w,-w2)
⇒ x=1-2,1-2w,1-2w2
⇒ x=-1,1-2w,1-2w2
Hence, Option ‘C’ is Correct.
if the cube root of unity are 1, w;w2,then the roots of the equation x-1 whole cube +8=0