uppose f() is a polýnomial with three zeros: 3 of multiplicity 1, - 2 of multiplicity 2, and a zero at I= - a zero at I= a zero at I = -1 of multiplicity 1. Finally, f(0) = 9 Key numbers and multiplicities. -5 -4 -3 -2 -1 2 3 4 (a) Where is f(r) > 0? Write your answer as a union of two intervals, e.g., (- ∞, – 1] U 4, 00). Note that [3, 4| U [4, 5] = [3, 5]. (b) Where is f(z) < 0? Write your answer as an interval, e.g.. 1, 5. (c) Make a sketch of the polynomial in your notebook.
uppose f() is a polýnomial with three zeros: 3 of multiplicity 1, - 2 of multiplicity 2, and a zero at I= - a zero at I= a zero at I = -1 of multiplicity 1. Finally, f(0) = 9 Key numbers and multiplicities. -5 -4 -3 -2 -1 2 3 4 (a) Where is f(r) > 0? Write your answer as a union of two intervals, e.g., (- ∞, – 1] U 4, 00). Note that [3, 4| U [4, 5] = [3, 5]. (b) Where is f(z) < 0? Write your answer as an interval, e.g.. 1, 5. (c) Make a sketch of the polynomial in your notebook.
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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![**Transcription for Educational Website:**
---
**Polynomial Analysis**
Suppose \( f(x) \) is a polynomial with three zeros:
- A zero at \( x = -3 \) of multiplicity 1,
- A zero at \( x = -2 \) of multiplicity 2, and
- A zero at \( x = -1 \) of multiplicity 1.
Finally, \( f(0) = 9 \).
**Key Numbers and Multiplicities:**
A number line is provided illustrating key points with their multiplicities:
- -3 (multiplicity 1)
- -2 (multiplicity 2)
- -1 (multiplicity 1)
These points are marked on the number line from -5 to 5.
---
**Questions for Analysis:**
(a) **Where is \( f(x) \geq 0 \)?**
Write your answer as a union of two intervals, e.g., \( (-\infty, -1] \cup [4, \infty) \).
Note: \([3, 4] \cup [4,5] = [3, 5]\).
(b) **Where is \( f(x) \leq 0 \)?**
Write your answer as an interval, e.g., \([1, 5]\).
(c) **Make a sketch of the polynomial in your notebook.**
---
This setup allows students to analyze the polynomial properties and visualize the behavior of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62c7af9b-7edb-4c2c-bdd3-301deede1977%2F37f22a4f-1eee-46fa-9e27-13829bd652d2%2Fjz3mm3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Polynomial Analysis**
Suppose \( f(x) \) is a polynomial with three zeros:
- A zero at \( x = -3 \) of multiplicity 1,
- A zero at \( x = -2 \) of multiplicity 2, and
- A zero at \( x = -1 \) of multiplicity 1.
Finally, \( f(0) = 9 \).
**Key Numbers and Multiplicities:**
A number line is provided illustrating key points with their multiplicities:
- -3 (multiplicity 1)
- -2 (multiplicity 2)
- -1 (multiplicity 1)
These points are marked on the number line from -5 to 5.
---
**Questions for Analysis:**
(a) **Where is \( f(x) \geq 0 \)?**
Write your answer as a union of two intervals, e.g., \( (-\infty, -1] \cup [4, \infty) \).
Note: \([3, 4] \cup [4,5] = [3, 5]\).
(b) **Where is \( f(x) \leq 0 \)?**
Write your answer as an interval, e.g., \([1, 5]\).
(c) **Make a sketch of the polynomial in your notebook.**
---
This setup allows students to analyze the polynomial properties and visualize the behavior of the function.
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