# Let z1, z2 be the roots of the equation

Question:

Let $z_{1}, z_{2}$ be the roots of the equation $z^{2}+a z+12=0$ and $\mathrm{z}_{1}, \mathrm{z}_{2}$ form an equilateral triangle with origin. Then, the value of lal is

Solution:

If $0, \mathrm{z}, \mathrm{z}_{2}$ are vertices of equilateral triangles

$\Rightarrow a^{2}+z_{1}^{2}+z_{2}^{2}=0\left(z_{1}+z_{2}\right)+z_{1} z_{2}$

$\Rightarrow\left(z_{1}+z_{2}\right)^{2}=3 z_{1} z_{2}$

$\Rightarrow a^{2}=3 \times 12$

$\Rightarrow|a|=6$