Caleb was determining the nature of the roots of the polynomial equation x* + 2x° +x +1 = 0. Follow Caleb's work below and identify his mistake. Then explain WHY it is wrong and show/tell Caleb how to correctly find the nature of the roots. Caleb's work/explanation: P(x) = x* + 2x +x +1 has 0 sign changes. P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes. Since there are no sign changes for P(x), there are no positive roots. Since there are no sign changes for P(-x), there are no negative roots. Since none of the roots are positive or negative, all four roots must be complex.
Caleb was determining the nature of the roots of the polynomial equation x* + 2x° +x +1 = 0. Follow Caleb's work below and identify his mistake. Then explain WHY it is wrong and show/tell Caleb how to correctly find the nature of the roots. Caleb's work/explanation: P(x) = x* + 2x +x +1 has 0 sign changes. P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes. Since there are no sign changes for P(x), there are no positive roots. Since there are no sign changes for P(-x), there are no negative roots. Since none of the roots are positive or negative, all four roots must be complex.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Topic Video
Question
see picture
![Caleb was determining the nature of the roots of the
2
polynomial equation x* + 2x° + x +1 = 0.
Follow Caleb's work below and identify his mistake.
Then explain WHY it is wrong and show/tell Caleb how
to correctly find the nature of the roots.
Caleb's work/explanation:
P(x) = x* + 2x +x +1 has 0 sign changes.
P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes.
Since there are no sign changes for P(x), there are no
positive roots.
Since there are no sign changes for P(-x), there are
no negative roots.
Since none of the roots are positive or negative, all four
roots must be complex.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10a9f489-d438-4273-b76d-cc8abf92d638%2F3394eebd-dfd2-49a0-81db-43df939f7dd8%2Fp9nxw9a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Caleb was determining the nature of the roots of the
2
polynomial equation x* + 2x° + x +1 = 0.
Follow Caleb's work below and identify his mistake.
Then explain WHY it is wrong and show/tell Caleb how
to correctly find the nature of the roots.
Caleb's work/explanation:
P(x) = x* + 2x +x +1 has 0 sign changes.
P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes.
Since there are no sign changes for P(x), there are no
positive roots.
Since there are no sign changes for P(-x), there are
no negative roots.
Since none of the roots are positive or negative, all four
roots must be complex.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education