If the cube roots of unity are 1, ω, ω^2 , then the roots of the equation (x - 1)^3 + 8 = 0 are: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

The given equation is: (x - 1)^{3} + 8 = 0 ⟹ (x - 1)^{3} = - 8 Taking the cube root on both sides: (x - 1) = (- 8)^{1/3} = - 2 (1)^{1/3} The cube roots of unity are 1, ω, ω^{2} . Therefore: (x - 1) = - 2 (1), - 2 (ω), or - 2 (ω^{2}) Solving for x : x - 1 = - 2 ⟹ x = - 1 x - 1 = - 2 ω ⟹ x = 1 - 2 ω x - 1 = - 2 ω^{2} ⟹ x = 1 - 2 ω^{2} Thus, the roots are - 1, 1 - 2 ω, 1 - 2 ω^{2} .

Try it yourself before checking the explanation above.

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

- 1, - 1 + 2 ω, - 1 - 2 ω^{2}

- 1, - 1, - 1

- 1, 1 - 2 ω, 1 - 2 ω^{2}

- 1, 1 + 2 ω, 1 + 2 ω^{2}

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