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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 26E
Related questions
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:**
\[ \text{Ans.} \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa610010-7ad2-4d49-b949-5d449ad446df%2F01c7d99f-3bdc-4e88-8bdc-05f65f969ede%2Fbbhnenn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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