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Let $z_{1}$ and $z_{2}$ be two roots of the equation $z^{2}+a z+b=0, z$ being complex. Further, assume that the origin, $z_{1}$ and $z_{2}$ form an equilateral triangle, then

1) $a^{2}=b$
2) $a^{2}=2 b$
3) $a^{2}=3 b$
4) $a^{2}=4 b$
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(3)

Explanation

$z_{1}^{2}+z_{2}^{2}-z_{1} z_{2}=0$
$\left(z_{1}+z_{2}\right)^{2}-3 z_{1} z_{2}=0$
$a^{2}=3 b$

by Diamond (75,948 points)

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