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

Given equation is z² + z + 1 – a = 0.

Clearly, this equation does not have real roots if

D < 0

⇒ 1 - 4(1 - a)< 0

⇒ 4a < 3

⇒ a  < 3/4