3.4.25 Find all rational zeros of the given polynomial function. 4 F(x) = x* - x° - 13x2 + x+ 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set of rational zeros of F(x) is { }. (Type integers or simplified fractions. Use a comma to separate answers as needed.) B. The given function has no rational zeros.
3.4.25 Find all rational zeros of the given polynomial function. 4 F(x) = x* - x° - 13x2 + x+ 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set of rational zeros of F(x) is { }. (Type integers or simplified fractions. Use a comma to separate answers as needed.) B. The given function has no rational zeros.
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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![### 3.4.25
**Objective:** Find all rational zeros of the given polynomial function.
The polynomial function is given by:
\[ F(x) = x^4 - x^3 - 13x^2 + x + 12 \]
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** The set of rational zeros of \( F(x) \) is \[ \{ \} \].
*(Type integers or simplified fractions. Use a comma to separate answers as needed.)*
- **B.** The given function has no rational zeros.
**Explanation:** To determine the set of rational zeros of the polynomial function, you may use the Rational Root Theorem, which states that any rational solution, \(\frac{p}{q}\), is a factor of the constant term divided by a factor of the leading coefficient. In this case, you will check the factors of 12 divided by the factors of 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdafe61fc-c70a-4579-bf5c-a90ac61b494b%2Fa6e1c75b-25e5-490e-b12c-6b049511d316%2Ffdqyn8_processed.png&w=3840&q=75)
Transcribed Image Text:### 3.4.25
**Objective:** Find all rational zeros of the given polynomial function.
The polynomial function is given by:
\[ F(x) = x^4 - x^3 - 13x^2 + x + 12 \]
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** The set of rational zeros of \( F(x) \) is \[ \{ \} \].
*(Type integers or simplified fractions. Use a comma to separate answers as needed.)*
- **B.** The given function has no rational zeros.
**Explanation:** To determine the set of rational zeros of the polynomial function, you may use the Rational Root Theorem, which states that any rational solution, \(\frac{p}{q}\), is a factor of the constant term divided by a factor of the leading coefficient. In this case, you will check the factors of 12 divided by the factors of 1.
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