Multiple choice

lf the cube roots of unity are 1,$\omega,\ \omega^{2}$, then the roots of the equation $(x-1)^{3}+8=0$, are

  1. $-1,1-2\omega, 1-2\omega^{2}$
  2. $-1,1+2\omega, 1+2\omega^{2}$
  3. $-1,-1+2\omega, -1-2\omega^{2}$
  4. $-1,1, -\omega$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(x-1)^3 = -8. Taking cube roots: x-1 = -2, -2w, -2w^2. x = -1, 1-2w, 1-2w^2.

AI explanation

We can rewrite the equation as (x - 1)^3 = -8, which implies x - 1 is equal to the cube roots of -8, specifically -2, -2*omega, and -2*omega^2. Adding 1 to each of these roots gives the values of x as -1, 1 - 2*omega, and 1 - 2*omega^2.

Keep practicing — related questions