Quadratic Inequlities

Introduction to quadratic inequalities:

A quadratic inequality in one variable is in the form of an expression:

ax² + bx + c ≤ 0 or ax² + bx + c <>2 + bx + c ≥ 0 or ax² + bx + c <>

where a, b and c are real numbers, a ≠ 0. The values of x which satisfy the given inequality are called the solutions of the inequality.
A quadratic equation has only two roots. But a quadratic inequality has many roots.

Methods of solving quadratic Inequalities

There are two methods in solving inequalities.

Method 1: Finding the solution by dividing the given polynomial into factors. This method is called the 'Algebraic method'.

Method 2: Finding the solutions by drawing the graph of the inequality. This method is called the 'Graphical method'.

Note:

• The trick in solving a quadratic inequality is to replace the inequality symbol with an equal sign and solve the resulting equation. The solutions to the equation will allow us to establish intervals that will let you solve the inequality.
• Plot the solutions on number line creating the intervals for investigation. Pick any number from each interval and test it in original inequality. If the result is true, that interval is the solution to the inequality.