### Polynomial Root AnalysisFor 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.

For polynomials with degree greater than 2,we need to find the roots by hit and trial. Factor out…

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

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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Concept explainers

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.

Question

### 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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