Solving Equations and Inequalities

General Mathematics — Second Secondary

Quadratic inequalities and sign tables

Make one side zero and factorise the quadratic expression into two factors.
Find the roots, that is the values that make the expression zero, and place them on the number line.
Test the sign of each interval between the roots with a value inside it, then choose the intervals that satisfy the inequality.
Example to solve (x − 3)(x + 2) > 0, the roots are −2 and 3. For x < −2 the product is positive, between −2 and 3 it is negative, and for x > 3 it is positive. So the solution is x < −2 or x > 3.

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