Solution assignment 09 Quadratic inequalities

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Assignment 9

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?

Solution

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.

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