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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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.
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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