GB-08-05-001 · Quadratic inequalities

Solve $x^{2} - 3x - 4>0$ .

Quadratic Inequalities Booklet p. 16

Method

1) Rearrange to get all terms to one side (x² positive)

2) Factorise to find critical values

3) Sketch U-shaped parabola

4) quadratic > 0 ⇒ x < a or x > b

Worked Example (GB-08-05-001)

1) Factorise to find critical values (Booklet p. 5 & p. 16):

×	$x$	$+1$
$x$	$x^2$	$+x$
$-4$	$-4x$	$-4$

a \times c = 1 \times (-4) = -4

$+1$	$-4$
$+2$	$-2$

c is negative so signs are different (+ and −)...

+1 - 4 = -3

✔

\text{Brackets: } \mathbf{(x - 4)(x + 1)}

2) Critical values:

x = -1

and

x = 4

3) Sketch graph: quadratic

> 0

(above axis)

\Rightarrow x < -1

x > 4

x<-1

x>4