Root of the equation $x^2+ix+2=0$ 
What are the roots of the equation $x^2+ix+2=0$, where $i=\sqrt{-1}$?

*

*$(-1, 1)$

*$(-2i, i)$

*$( i, 1)$

*no root exists


I don't know the method for finding roots of this type of equation.
I  have tried by the method of $b^2-4ac$ but it doesn't work

Use the quadratic formula:
\begin{align}x&=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\
&=\frac{-i\pm\sqrt{i^2-4\times 2}}{2}\\
&=\frac{-i\pm\sqrt{(-1)-8}}{2}\\
&=\frac{-i\pm\sqrt{-9}}{2}\\
&=\frac{-i\pm i\sqrt{9}}{2}\\
&=\frac{-i\pm3i}{2}\end{align}
So we have $$x=\frac{-i+3i}{2}=\frac{2i}{2}=i$$ and $$x=\frac{-i-3i}{2}=\frac{-4i}{2}=-2i$$
So our roots are $(-2i,i)$
