Question

Let z be a complex number such that the imaginary part of z is non–zero and a = z² + z + 1 is real. Then a cannot take the value

(a) –1

(b) 1/3

(c) 1/2

(d) 3/4

Answer 1

Correct option (d)

Explanation:

Given equation is z² + z + 1 – a = 0

Clearly this equation do not have real roots if D < 0

⇒ 1 - 4(1 - a) < ⇒ 4a < 3 ⇒ a < 3/4