Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero h(x) = x²9x³ + 23x² − 33x + 18 1-√2i X =
Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero h(x) = x²9x³ + 23x² − 33x + 18 1-√2i X =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![### Finding All Zeros of the Polynomial Function
#### Problem Statement:
Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.)
**Function:**
\[ h(x) = x^4 - 9x^3 + 23x^2 - 33x + 18 \]
**Given Zero:**
\[ 1 - \sqrt{2}i \]
#### Solution:
Please input your solution in the box below:
\[ x = \boxed{} \]
---
#### Additional Explanation:
When you find a complex zero of a polynomial with real coefficients, its conjugate is also a zero. If \(1 - \sqrt{2}i\) is a zero, then \(1 + \sqrt{2}i\) is also a zero. Using these zeros, you can perform polynomial division or use synthetic division to find the remaining zeros.
The process involves:
1. Verifying that both \(1 - \sqrt{2}i\) and \(1 + \sqrt{2}i\) are zeros.
2. Using these zeros to factor the polynomial and reduce its degree.
3. Solving the reduced polynomial to find the remaining real or complex zeros.
Feel free to enter your calculations and final answers in the provided input box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb5ff0f4-c9f6-49ea-9161-fbb64a60fa05%2Fbcdbf4cb-ba09-4f8c-86ec-8c80e89188a9%2F9inw9xj_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding All Zeros of the Polynomial Function
#### Problem Statement:
Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.)
**Function:**
\[ h(x) = x^4 - 9x^3 + 23x^2 - 33x + 18 \]
**Given Zero:**
\[ 1 - \sqrt{2}i \]
#### Solution:
Please input your solution in the box below:
\[ x = \boxed{} \]
---
#### Additional Explanation:
When you find a complex zero of a polynomial with real coefficients, its conjugate is also a zero. If \(1 - \sqrt{2}i\) is a zero, then \(1 + \sqrt{2}i\) is also a zero. Using these zeros, you can perform polynomial division or use synthetic division to find the remaining zeros.
The process involves:
1. Verifying that both \(1 - \sqrt{2}i\) and \(1 + \sqrt{2}i\) are zeros.
2. Using these zeros to factor the polynomial and reduce its degree.
3. Solving the reduced polynomial to find the remaining real or complex zeros.
Feel free to enter your calculations and final answers in the provided input box.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
