Wetzel                                                                                    

Math 102

10.6 – Quadratic and Rational Inequalities

Quadratic Inequalities: 

            Steps to Solve:

                        1.)  Solve the inequality as if it were an equation.

                        2.)  Graphs these points and a number line and determine the different intervals.

                        3.)  Choose a test point from each interval and see if it is a solution to the inequality.

                        4.)  The intervals where the test points are true are the solutions to the inequality.  Write the solution in interval notation.

Example:

 1.)                                        2.) 

Rational Inequalities:

            Steps to Solve:

                        1.)  Get ONE rational on the left side of the inequality sign and zero on the right side.

                        2.)  Set the numerator = 0 and solve.  Set the denominator =0 and solve. These values are called the zeros.

                        3.)  Graphs these points and a number line and determine the different intervals.

                        4.)  Choose a test point from each interval and see if it is a solution to the rational.

                        5.)  The intervals where the test points are true are the solutions to the rational.  Write the solution in interval notation.

                        **Note:  If the zero came from the denominator, it must have ( ) next to it.

Examples:

1.)                2.)               3.)