In an Argand plane, $A(z_1), B(z_2), C(z_3)$ are distinct complex numbers lying on the curve $\;|z| = \sqrt 3$.
If a root of $z_1z^2 + z_2z + z_3 = 0$ has a modulus equal to unity then $z_1, z_2, z_3$ are in
a) Arithmetic progression
b) Geometric Progression
c) Harmonic Progression
d) All of these
Firstly I assumed root to be $a$ and then put it in the equation. Then I took the conjugate of the whole equation as $\bar a= 1/a$ and $\bar z_i= 3/z_i\; (i=1,2,3)$. I have concluded the other root to be unimodular as well and the angle between roots is 120 deg but I am unable to get a relation between $z_1,z_2,z_3$.