Find roots of polynomial $$ p(x) = z^2+z+1 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= -\frac{ 1 }{ 2 }+\frac{\sqrt{ 3 }}{ 2 }i\\[1 em]z_2 &= -\frac{ 1 }{ 2 }- \frac{\sqrt{ 3 }}{ 2 }i \end{aligned} $$Explanation
The solutions of $ z^2+z+1 = 0 $ are: $ z = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i ~ \text{and} ~ z = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 3 }}{ 2 }i$.
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