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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 ____________.
Option: 1 2
Option: 2 4
Option: 3 6
Option: 4 8

Answers (1)

best_answer

0, z1, z2 are the vertex of the equilateral triangle

\begin{aligned} &\text { for equilateral triangle }\\ &z_{1}^{2}+z_{2}^{2}+O^{2}=z_{1} z_{2}+0+0\\ &\left(\mathrm{z}_{1}+\mathrm{z}_{2}\right)^{2}=3 \mathrm{z}_{1} \mathrm{z}_{2}\\ &\Rightarrow\left(-a^{2}\right)=3(12)\\ &\Rightarrow \mathrm{a}^{2}=36\\ &\mathrm{a}=-6 \text { or } 6\\ &|\mathrm{a}|=6 \end{aligned}

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