Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 3 (multiplicity 2), 5+i (multiplicity 1) f(x) =
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 3 (multiplicity 2), 5+i (multiplicity 1) f(x) =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed
3 (multiplicity 2), 5 + i (multiplicity 1)
![Title: Writing Polynomial Functions with Given Zeros and Multiplicities
---
**Objective:**
Learn how to write a polynomial function of minimum degree with real coefficients, given the zeros and their respective multiplicities.
**Problem Statement:**
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed:
- 3 (multiplicity 2)
- 5 + i (multiplicity 1)
**Instructions:**
1. Simplify your answer.
2. Do not factor.
3. Use integers or fractions for any numbers in the expression.
**Solution:**
Write the polynomial function \( f(x) \): \[ \boxed{\square} \]
Remember, zeros with complex numbers such as \( 5 + i \) require their conjugates \( 5 - i \) to be included to ensure all coefficients are real.
---
This exercise guides you on understanding how complex roots appear in conjugate pairs when forming polynomial expressions with real coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7d6490b-851a-4cd6-a7a2-4767e7edc316%2F8d94e65c-44df-4c8b-8ee5-517af3169af7%2Fe0os062_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Writing Polynomial Functions with Given Zeros and Multiplicities
---
**Objective:**
Learn how to write a polynomial function of minimum degree with real coefficients, given the zeros and their respective multiplicities.
**Problem Statement:**
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed:
- 3 (multiplicity 2)
- 5 + i (multiplicity 1)
**Instructions:**
1. Simplify your answer.
2. Do not factor.
3. Use integers or fractions for any numbers in the expression.
**Solution:**
Write the polynomial function \( f(x) \): \[ \boxed{\square} \]
Remember, zeros with complex numbers such as \( 5 + i \) require their conjugates \( 5 - i \) to be included to ensure all coefficients are real.
---
This exercise guides you on understanding how complex roots appear in conjugate pairs when forming polynomial expressions with real coefficients.
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