Question

$z_1$ and $z_2$ are the roots of 3$z^2$ + 3z + b = 0. If O(0), A($z_1$)B($z_2$) is an equilateral triangle, then

• A. b= -1
• B. b= -3
• C. b=1
• D. b=3

Answer 1

The correct option is C

b=1

$z_1+z_2$ = -1, $z_1.z_2$ = $\frac{b}{3}$

O, $A\left(z_1\right),B+\left(z_2\right)$ form an equilateral triangle. Therefore

$0+z_1^2+z_2^2+0.z_2+z_1{z}_2$

$\Rightarrow$ $(z_1+z_2{)}^2$ = $3z_1{z}_2$ $\Rightarrow$ 1 = b