Assignments

In order to solve quadratic inequalities, it is necessary that you know how to solve quadratic equations, see also Quadratic equations (abc-formula) and Quadratic equations (factorizing). An important quantity is the discriminant. Following a series of assignments in which these aspects are important.

1. Solve:

$x^2+7x+12\leq0$

2. Solve:

$-x^2+5x-6>0$

3. Solve:

$x^2-x-56<0$

4. Solve:

$3x^2+x-2\geq0$

5. Solve:

$-4x^2-8x<0$

6. Solve:

$4x^2+20x+25\geq0$

7. Solve:

$x^2+x+25<0$

8. For which value(s) of $x$ does the following inequality hold:

$x^2+25>0$

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?

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

$P: y=x^2-1$

and the line:

$l: y=x+a$

have no points in common?

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