Cambridge O Level Additional Mathematics · Syllabus 4037 · Quadratic Functions
Quadratic Inequality
What is Quadratic Inequality?
An inequality in which a quadratic expression is compared with zero, such as ax^2 + bx + c less than or equal to zero. Its answer is a solution set, not a pair of numbers: the set of all x for which the statement is true. The roots of the corresponding equation are the critical values where the expression changes sign, and the opening direction of the parabola then decides whether the wanted region lies between those roots or outside them. Endpoints belong to the set only when the inequality is non-strict.
This definition is part of the Quadratic Functions chapter in Cambridge O Level Additional Mathematics.
Questions students ask about Quadratic Inequality
How do you solve a quadratic inequality?
Rearrange so one side is zero, find the roots of the corresponding equation (the critical values), then use the shape of the parabola or a sign diagram to decide which region is wanted. An upward parabola is negative between its roots and positive outside them, so \(x^2-x-6>0\) gives \(x<-2\) or \(x>3\). Never split a product inequality into two separate factor inequalities, and copy the endpoint convention: \(\le\) and \(\ge\) include the roots, \(<\) and \(>\) exclude them.