If \( z_{1} \) and \( z_{2} \) are the roots of the equation \( z^{...

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If \( z_{1} \) and \( z_{2} \) are the roots of the equation \( z^{2}+a z+ \) \( b=0 \), then prove that the origin, \( z_{1} \) and \( z_{2} \) form an equilateral triangle if and only if
(a) \( a^{2}=3 b \)
(b) \( b^{2}=3 a \)
(c) \( a^{2}+3 b=0 \)
(d) \( b^{2}+3 a=0 \)
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