Question

Let $z _1, z _2$ be the roots of the equation $z ^2+ az +$ $12=0$ and $z _1, z _2$ form an equilateral triangle with origin. Then, the value of $|a|$ is

Answer 1

$\text { If } 0, z, z_2 \text { are vertices of equilateral triangles }$
$\Rightarrow a^2+z_1^2+z_2^2=0\left(z_1+z_2\right)+z_1 z_2 $
$\Rightarrow\left(z_1+z_2\right)^2=3 z_1 z_2 $
$\Rightarrow a^2=3 \times 12$
$\Rightarrow|a|=6$