Question:
$x^{2}+x+1=0$
Solution:
Given:
$x^{2}+x+1=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-1 \pm \sqrt{1^{2}-(4 \times 1 \times 1)}}{2 \times 1}$
$\Rightarrow x=\frac{-1 \pm \sqrt{1-4}}{2}$
$\Rightarrow x=\frac{-1 \pm \sqrt{-3}}{2}$
$\Rightarrow x=\frac{-1 \pm \sqrt{3} i}{2}$
$\Rightarrow \quad x=-\frac{1}{2} \pm \frac{\sqrt{3}}{2} i$
Ans: $x=-\frac{1}{2}+\frac{\sqrt{3}}{2} i$ and $x=-\frac{1}{2}-\frac{\sqrt{3}}{2} i$