Let a, b in mathbb{R} and the roots alpha, be | vedclass

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(B) Given that $\alpha$ and $\beta$ are roots of the equation $z^2+az+b=0$.From the properties of roots,we have $\alpha+\beta = -a$ and $\alpha\beta =

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$a^2=3b$

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(B) Given that $\alpha$ and $\beta$ are roots of the equation $z^2+az+b=0$.From the properties of roots,we have $\alpha+\beta = -a$ and $\alpha\beta = b$.Since the origin $(0)$,$\alpha$,and $\beta$ form an equilateral triangle in the Argand plane,the condition for an equilateral triangle with one vertex at the origin is $\alpha^2 + \beta^2 = \alpha\beta$.We can rewrite this as $(\alpha+\beta)^2 - 2\alpha\beta = \alpha\beta$.Substituting the values of the sum and product of roots: $(-a)^2 - 2(b) = b$.This simplifies to $a^2 - 2b = b$,which gives $a^2 = 3b$.

Let $a, b \in \mathbb{R}$ and the roots $\alpha, \beta$ of the equation $z^2+az+b=0$ be complex. If the origin,$\alpha$ and $\beta$ represent the vertices of an equilateral triangle on the Argand plane,then

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