To Describe: The graphs of possible solutions of the given inequality.
The graphs of possible solutions of the given inequality have been described.
Given:
The inequality,
Concept used:
The solutions of a cubic inequality depend on the number of real roots of the corresponding cubic equation.
Calculation:
The given inequality is
The corresponding cubic equation is
Now, the following two cases may arise:
Case 1:
Then the equation can be factorized as
So, the corresponding inequality is
Let arbitrarily
If
The graph of this would be the union of two disjoint open intervals on the real line.
If
The graph of this would again be the union of two disjoint open intervals on the real line.
Case 2:
Then, the equation can be factorized as
So, the corresponding inequality is
If
The graph of this would be an open interval on the real line extending infinitely to the right.
If
The graph of this would again be an open interval on the real line, but extending infinitely to the left.
Conclusion:
The graphs of possible solutions of the given inequality have been described.
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education