If f (x) is a polynomial with real coefficients and zeros of 3 (multiplicity 1), -1 (multiplicity 2), -1+2i, and 3-5i, what is the minimum degree of f (x)? The minimum degree of f (x) is

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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**Polynomial Degree Problem**

If \( f(x) \) is a polynomial with real coefficients and zeros of 3 (multiplicity 1), −1 (multiplicity 2), \( -1 +2i \), and \( 3-5i \), what is the minimum degree of \( f(x) \)?

*Note*: The zeros of the polynomial include real numbers (3 and -1) and complex numbers (-1 + 2i and 3 - 5i).

**Question**: The minimum degree of \( f(x) \) is ___.

*(Insert an answer box here for user input, followed by clear buttons for submission and reset.)*

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**Explanation of the Elements**:

- **Text and Problem Statement**: Clearly states the nature of the polynomial and its zeros.
  
- **Input Box**: Provides a space for students to input their answer to the posed question.
  
- **Buttons**: There are two buttons, one with an "X" to possibly delete the input, and another with a rotating arrow, likely to reset the question or start over.

---

This layout guides students through identifying the minimum degree of a polynomial given specific zeroes, including their multiplicity and complex nature. Ideal for educational purposes, it provides clear instructions and an interactive element to reinforce learning.
Transcribed Image Text:**Polynomial Degree Problem** If \( f(x) \) is a polynomial with real coefficients and zeros of 3 (multiplicity 1), −1 (multiplicity 2), \( -1 +2i \), and \( 3-5i \), what is the minimum degree of \( f(x) \)? *Note*: The zeros of the polynomial include real numbers (3 and -1) and complex numbers (-1 + 2i and 3 - 5i). **Question**: The minimum degree of \( f(x) \) is ___. *(Insert an answer box here for user input, followed by clear buttons for submission and reset.)* --- **Explanation of the Elements**: - **Text and Problem Statement**: Clearly states the nature of the polynomial and its zeros. - **Input Box**: Provides a space for students to input their answer to the posed question. - **Buttons**: There are two buttons, one with an "X" to possibly delete the input, and another with a rotating arrow, likely to reset the question or start over. --- This layout guides students through identifying the minimum degree of a polynomial given specific zeroes, including their multiplicity and complex nature. Ideal for educational purposes, it provides clear instructions and an interactive element to reinforce learning.
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