**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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Answered: If f (x) is a polynomial with real…

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

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.CT: Chapter Test

Problem 9CT

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.

Question

**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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