Let z1 and z2 be two roots of the equation z^2 + az + b = 0

Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex further, assume that the origin, z1 and z2 form an equilateral triangle, then

  1. a2 = 4b
  2. a2 = 3b
  3. a2 = 2b
  4. a2 = b

Answer

As z1, z2 are roots of z2 + az + b

z1 + z2 = –a and z1 z2 = b

Again 0, z1,  z2 are vertices of an equilateral triangle.

Therefore, 02 + z12 + z22 = 0z1 + z1z2 + 0z2 = 0

z12 + z22 = z1z2

(z1 + z2)2 = 3z1z2

The correct option is B.