Using Changes of Sign to Solve Quadratic Inequalities

To solve a quadratic inequality, we can simplify and factorise it and analyse the sign change of each factor, hence the sign change of the quadratic, to solve it.

For example, to solvefactorise to give

has a sign change at

has a sign change at

Now use the ordinary rules of sign multiplication:

to draw a sign change digram for

From this diagram,for