In the following, determine whether the given quadratic equations have real roots and if so, find the roots:

$x^2+x+2=0$

Given:

Given quadratic equation is $x^2+x+2=0$.

To do:

We have to determine whether the given quadratic equation has real roots.

Solution:

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=1, b=1$ and $c=2$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is

$D=b^2-4ac$.

Therefore,

$D=(1)^2-4(1)(2)=1-4=-3$.

As $D<0$, the given quadratic equation has no real roots.