Solve this

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 $x=-\frac{1}{2}-\frac{\sqrt{3}}{2} i$

 

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