Question
Question: If the cube roots of unity are 1, ω, ω<sup>2</sup>, then the roots of the equation (x – 1)<sup>3</su...
If the cube roots of unity are 1, ω, ω2, then the roots of the equation (x – 1)3 + 8 = 0 are
A
– 1, 1 + 2ω, 1 + 2ω2
B
–1, 1 – 2ω, 1 – 2ω2
C
–1, –1, –1
D
None of these
Answer
–1, 1 – 2ω, 1 – 2ω2
Explanation
Solution
Sol. (x – 1)3 + 8 = 0 ⇒ (x – 1)3 = – 8
⇒ x – 1 = (– 8)1/3 = –2, –2ω, – 2ω2
⇒ x = – 1, 1 – 2ω, 1 – 2ω2