Question:
Let $\mathrm{z}_{1}, \mathrm{z}_{2}$ be the roots of the equation $\mathrm{z}^{2}+\mathrm{az}+$ $12=0$ and $\mathrm{z}_{1}, \mathrm{z}_{2}$ form an equilateral triangle with origin. Then, the value of lal is
Solution:
If $0, \mathrm{z}, \mathrm{z}$, are vertices of equilateral triangles
$\Rightarrow a^{2}+z_{1}^{2}+z_{2}^{2}=0\left(z_{1}+z_{2}\right)+z_{1} z_{2}$
$\Rightarrow\left(z_{1}+z_{2}\right)^{2}=3 z_{1} z_{2}$
$\Rightarrow a^{2}=3 \times 12$
$\Rightarrow|a|=6$
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