Solution assignment 09 Quadratic inequalities

For which value(s) of $a$ do the parabola:

$P: y=x^2+x-2$

and the line:

$l: y=a$

have no points in common?

First we calculate the intersection points of $P$ and $l$ . Thus we have to solve:

$x^2+x-2=a$

This equation may not have common points so the discriminant of quadratic equation has to be less than $0$ :

$D=1+4(2+a)<0$

$a<-\displaystyle\frac{9}{4}$

For these values of $a$ the parabola $P$ and the line $l$ have no common points.