Tell the maximum number of zeros that the polynomial function may have. Then use real zeros the polynomial function may have. Do not attempt to find the zeros: 8. f(x) = - 5x° +2x° -6 What is the maximum number of zeros that this polynomial function can have? How many positive real zeros can the function have? (Use a comma to separate answers as needed.) How many negative real zeros can the function have? (Use a comma to separate answers as needed.)

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 Function Analysis**

In this exercise, you are tasked with determining information about the zeros of a polynomial function. The given polynomial is:

\[ f(x) = -5x^8 + 2x^6 - 6 \]

### Questions to Consider:

1. **What is the maximum number of zeros that this polynomial function can have?**
   - The degree of the polynomial informs the maximum possible number of zeros. For this polynomial, the degree is 8, meaning it can have up to 8 zeros.

2. **How many positive real zeros can the function have?**
   - Use Descartes' Rule of Signs to determine the potential number of positive real zeros. List your answers with commas separating any possibilities.

3. **How many negative real zeros can the function have?**
   - Again, use Descartes' Rule of Signs to determine the potential number of negative real zeros. Provide your answers separated by commas.

**Note:** Please enter your answers in each of the provided answer boxes. Descartes' Rule of Signs helps predict the number of positive and negative real zeros based on sign changes. Do not attempt to find the exact zeros; focus on determining the possibilities based on the function’s characteristics.
Transcribed Image Text:**Polynomial Function Analysis** In this exercise, you are tasked with determining information about the zeros of a polynomial function. The given polynomial is: \[ f(x) = -5x^8 + 2x^6 - 6 \] ### Questions to Consider: 1. **What is the maximum number of zeros that this polynomial function can have?** - The degree of the polynomial informs the maximum possible number of zeros. For this polynomial, the degree is 8, meaning it can have up to 8 zeros. 2. **How many positive real zeros can the function have?** - Use Descartes' Rule of Signs to determine the potential number of positive real zeros. List your answers with commas separating any possibilities. 3. **How many negative real zeros can the function have?** - Again, use Descartes' Rule of Signs to determine the potential number of negative real zeros. Provide your answers separated by commas. **Note:** Please enter your answers in each of the provided answer boxes. Descartes' Rule of Signs helps predict the number of positive and negative real zeros based on sign changes. Do not attempt to find the exact zeros; focus on determining the possibilities based on the function’s characteristics.
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