For the given polynomial o find the maximum possible umbers of the positive and the negative roots o find all the integer roots o find the non-integer real roots o find the complex roots a(x)=2x+5x++11x-49x-31x -26

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,...
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### Polynomial Root Analysis

For the given polynomial, perform the following tasks:

- Determine the maximum possible numbers of the positive and the negative roots.
- Identify all the integer roots.
- Find the non-integer real roots.
- Determine the complex roots.

The given polynomial is:

\[ a(x) = 2x^5 + 5x^4 + 11x^3 - 49x^2 - 31x + 26 \]

### Tasks:

1. **Find the maximum possible number of positive roots:**
   - [ ]
  
2. **Find the maximum possible number of negative roots:**
   - [ ]

3. **Identify all the integer roots:**
   - Example: \(x = 3\), \(x = -5\)
  
4. **Determine the non-integer real roots:**
   - Example: \(x = 3\), \(x = -5\)

5. **Determine the complex roots:**
   - Example: \(x = 3\), \(x = -5\)
    
### Instructions for completing the table:

1. For each category above (positive roots, negative roots, integer roots, non-integer real roots, and complex roots), analyze the polynomial to find the respective values.
2. Fill in the provided boxes with the correct values for the maximum possible numbers and the identified roots.

---

To learn more about polynomials and their roots, refer to the Polynomials section in our resources.
Transcribed Image Text:### Polynomial Root Analysis For the given polynomial, perform the following tasks: - Determine the maximum possible numbers of the positive and the negative roots. - Identify all the integer roots. - Find the non-integer real roots. - Determine the complex roots. The given polynomial is: \[ a(x) = 2x^5 + 5x^4 + 11x^3 - 49x^2 - 31x + 26 \] ### Tasks: 1. **Find the maximum possible number of positive roots:** - [ ] 2. **Find the maximum possible number of negative roots:** - [ ] 3. **Identify all the integer roots:** - Example: \(x = 3\), \(x = -5\) 4. **Determine the non-integer real roots:** - Example: \(x = 3\), \(x = -5\) 5. **Determine the complex roots:** - Example: \(x = 3\), \(x = -5\) ### Instructions for completing the table: 1. For each category above (positive roots, negative roots, integer roots, non-integer real roots, and complex roots), analyze the polynomial to find the respective values. 2. Fill in the provided boxes with the correct values for the maximum possible numbers and the identified roots. --- To learn more about polynomials and their roots, refer to the Polynomials section in our resources.
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