Question

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, –1
(b) –1, –1 + 2ω, –1 – 2ω²
(c) –1, 1 + 2ω, 1 + 2ω²
(d) –1, 1 – 2ω, 1 – 2ω² .

Answer 1

(d) : Method (1) : (By making the equation from the given roots)
Let us consider x = –1, –1, –1
∴ Required equation from given roots is
(x + 1)(x + 1)(x + 1) = 0
(x + 1)³ = 0 which does not match with the given equation
(x – 1)³ + 8 = 0 so x = –1, –1, –1 cannot be the proper choice.
Again consider x = –1, –1 + 2ω, –1 –2ω²
∴ Required equation from given roots is