Home
Linear Equations and Inequalitie
Solving Inequalities
Absolute Value Inequalities
Graphing Equivalent Fractions Lesson Plan
Investigating Liner Equations Using Graphing Calculator
Graphically solving a System of two Linear Equatio
Shifting Reflecting Sketching Graph
Graphs of Rational Functions
Systems of Equations and Inequalities
Graphing Systems of Linear Equat
LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS
Solving Inequalities with Absolute Values
Solving Inequalities
Solving Equations & Inequalities
Graph the rational function
Inequalities and Applications
Inequalities
Using MATLAB to Solve Linear Inequalities
Equations and Inequalities
Graph Linear Inequalities in Two Variables
Solving Equations & Inequalities
Teaching Inequalities:A Hypothetical Classroom Case
Graphing Linear Inequalities and Systems of Inequalities
Inequalities and Applications
Solving Inequalities
Quadratic Inequalities
Inequalities
Solving Systems of Linear Equations by Graphing
Systems of Equations and Inequalities
Graphing Linear Inequalities
Inequalities
Solving Inequalities
Solving Inequalities
Solving Equations Algebraically and Graphically
Graphing Linear Equations
Solving Linear Equations and Inequalities Practice Problems
Graphing Linear Inequalities
Equations and Inequalities
Solving Inequalities

QUADRATIC INEQUALITIES

Definition

Quadratic inequalities in one variable are inequalities which can be written in one of
the following forms:

where a, b and c are real numbers.

Procedure

Solving Quadratic Inequalities

1. Move all terms to one side.
2. Simplify and factor the quadratic expression.
3. Find the roots of the corresponding quadratic equation.
4. Use the roots to divide the number line into regions.
5. Test each region using theinequality.

Example 1 Solve the inequality, x^2 > x + 2 .

Solution

The corresponding equation is (x - 2)(x + 1) = 0 so…

Now we test one point in each region.

Region Test Point Inequality Status
I x = -2 (x - 2)(x + 1) = (-2 - 2)(-2 + 1) = 4 > 0 True
II x = 0 (x - 2)(x + 1) = (0 - 2)(0 + 1) = -2 > 0 False
III x = 3 (x - 2)(x + 1) = (3 - 2)(3 + 1) = 4 > 0 True

So the solution to this inequality is x < -1 or x > 2.

Example 2 Solve the inequality,

Solution

The corresponding equation is (x - 1)(x - 5) = 0 so…

Now we check one point in each region.

Region Test Point Inequality Status
I x = 0 (x - 1)(x - 5) = (0 - 1)(0 - 5) = 5 < 0 False
II x = 2 (x - 1)(x - 5) = (2 - 1)(2 - 5) = -3 < 0 True
III x = 6 (x - 1)(x - 5) = (6 - 1)(6 - 5) = 5 < 0 False

So the solution to this inequality is 1 ≤ x ≤ 5.

§4-2 PROBLEM SET

Solve each quadratic inequality, and graph the solution on a number line.

§4-2 PROBLEM SOLUTIONS