### Polynomial Root Problems#### Problem 5:**Task:** Use Descartes' Rule of Signs to determine the possible number of positive and negative roots of the polynomial $ f(x) = 6x^5 - 6x^3 + 10x + 5 $.**Answer:** \[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]#### Problem 6:**Task:** List all possible rational zeros of the polynomial $ f(x) = 3x^5 + 2x^2 - 3x + 2 $.**Answer:** \[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]#### Problem 7:**Task:** Find all the zeros of the polynomial $ x^4 - 6x^3 + 14x^2 - 54x + 45 = 0 $.**Answer:** \[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]#### Problem 8:**Task:** Find a fourth-degree polynomial that has zeros of 3, -3, and $ i $.**Answer:** \[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]

Answered: Image /qna-images/answer/01c7d99f-3bdc-4e88-8bdc-05f65f969ede.jpg

5. Use Descarte's Rule of Signs to determine the possible number of positive and negative roots of f(x) = 6x Ans. 6. List all possible rational zeros of f(x) = 3x + 2x - 3x + 2. %3D Ans. 7. Find all the zeros of x*- 6x + 14x 54x + 45 = 0. . %3D Ans. 8. Find a fourth degree polynomial that has zeros of 3, -3, i. Ans.

5. Use Descarte's Rule of Signs to determine the possible number of positive and negative roots of f(x) = 6x Ans. 6. List all possible rational zeros of f(x) = 3x + 2x - 3x + 2. %3D Ans. 7. Find all the zeros of x*- 6x + 14x 54x + 45 = 0. . %3D Ans. 8. Find a fourth degree polynomial that has zeros of 3, -3, i. Ans.

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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Question

### Polynomial Root Problems

#### Problem 5:
**Task:** Use Descartes' Rule of Signs to determine the possible number of positive and negative roots of the polynomial $ f(x) = 6x^5 - 6x^3 + 10x + 5 $.

**Answer:**
\[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]

#### Problem 6:
**Task:** List all possible rational zeros of the polynomial $ f(x) = 3x^5 + 2x^2 - 3x + 2 $.

**Answer:**
\[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]

#### Problem 7:
**Task:** Find all the zeros of the polynomial $ x^4 - 6x^3 + 14x^2 - 54x + 45 = 0 $.

**Answer:**
\[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]

#### Problem 8:
**Task:** Find a fourth-degree polynomial that has zeros of 3, -3, and $ i $.

**Answer:**
\[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]

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