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Welcome to our Math lesson on Solving Quadratic Inequalities, this is the second lesson of our suite of math lessons covering the topic of Quadratic Inequalities, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Solving Quadratic Inequalities
Solving a quadratic inequality means finding the set of values of the variable, which makes the inequality true. For example, the numbers 6, 7, 8, etc., are all solutions of the quadratic inequality x2 - 5x - 3 > 0 because for x = 6,
62 - 5 ∙ 6 - 3 > 0
36 - 30 - 3 > 0
3 > 0 (true)
For x = 7,
72 - 5 ∙ 7 - 3 > 0
49 - 35 - 3 > 0
11 > 0 (true)
For x = 8,
82-5 ∙ 8 - 3 > 0
64 - 40 - 3 > 0
21 > 0 (true)
On the other hand, for x = 5, we have
52 - 5 ∙ 5 - 3 > 0
25 - 25 - 3 > 0
-3 > 0 (false)
For x = 4,
42-5 ∙ 4 - 3 > 0
16 - 20 - 3 > 0
-7 > 0 (false)
and so on.
Example 2
Check whether the numbers -2, 0 and 3 are solutions for the quadratic inequality
2x2 - 3x - 1 ≥ 0
or not.
Solution 2
For x = -2, we have
2x2 - 3x - 1 ≥ 0
2 ∙ (-2)2 - 3 ∙ (-2) - 1 ≥ 0
2 ∙ 42 - 3 ∙ 4 - 1 ≥ 0
32 - 12 - 1 ≥ 0
19 ≥ 0 (true)
For x = 0, we have
2x2 - 3x - 1 ≥ 0
2 ∙ 02 - 3 ∙ 0 - 1 ≥ 0
0 - 0 - 1 ≥ 0
-1 ≥ 0 (false)
For x = 3, we have
2x2 - 3x - 1 ≥ 0
2 ∙ 32 - 3 ∙ 3 - 1 ≥ 0
2 ∙ 9 - 3 ∙ 3 - 1 ≥ 0
18 - 9 - 1 ≥ 0
8 ≥ 0 (true)
More Quadratic Inequalities Lessons and Learning Resources
Inequalities Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 10.2 | Quadratic Inequalities | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 10.2.1 | What are Quadratic Inequalities? | | |
| 10.2.2 | Solving Quadratic Inequalities | | |
| 10.2.3 | Solving Quadratic Inequalities by Studying the Sign | | |
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- Continuing learning inequalities - read our next math tutorial: Graphing Inequalities
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