Question

Solve $x^2+x+1=0$

Answer 1

Step 1 : Given, $x^2+x+1=0$

Step 2 : checking nature of roots
$D=b^2-4ac,a=1,b=1,c=1$
$\Rightarrow D=1-4=-3<0$
$\therefore D$ is negative.
$\therefore$ Roots are imaginary, so we can use the quadratic method.

Step 3 : Using quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
By putting the value of $a,b,c$
$x=\frac{-1\pm \sqrt{1-4}}{2}\Rightarrow \frac{-1\pm \sqrt{3}i}{2}(\because \sqrt{-1}=i)$

The values of $x$ are $\frac{-1+\sqrt{3}i}{2},\frac{-1-\sqrt{3}i}{2}$