Question

Let $z_1$ and $z_2$ be the complex roots of the equation ${3z}^2+3z+b=0$, if the origin together with the points represented by $z_1$ and $z_2$ form an equilateral triangle then the value of b is

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is C 3

$3z^2+3z+b=0$

$\therefore z^2+az+b=0$

As in equilateral $\Delta$

$a^2=3b$

$\therefore a=3$

$3^2=3b$

$b=\frac{9}{3}=3$.