Smpily by moltipyong (x + 6i)(x-6i) paygomia with こro X-9。 End a
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%
Transcribed Image Text:### Complex Numbers and Quadratic Functions
#### Problem 5: Simplify a Square Root with i
- **Task:** Write and simplify \(\sqrt{-48}\); include the use of \(i\).
#### Problem 6: Find the Zeros of a Quadratic Function
- **Task:** Find the zeros of the function \(y = 2x^2 + x + 7\). Write any complex zeros with \(i\).
![### Polynomial Simplification and Zero-Finding
#### Exercise 1: Simplify by Multiplying
\[ (x + 6i)(x - 6i) \]
In this problem, we need to simplify the expression by multiplying the two binomials.
#### Exercise 2: Finding a Polynomial with a Given Zero
\[ \text{Find a polynomial with zero } x = 4i. \]
In this problem, we need to find a polynomial such that \( x = 4i \) is one of its zeros.
Note: In the second exercise, some text is unreadable due to a scribble, but the instruction is clear about finding a polynomial with a specified zero.
### Steps for Exercise 1:
1. Distribute the terms in the binomials.
2. Apply the difference of squares formula where applicable.
3. Simplify the resulting expression.
### Steps for Exercise 2:
1. Use the fact that for a polynomial to have a non-real zero \( x = 4i \), the conjugate \( x = -4i \) must also be a zero.
2. Formulate the polynomial by combining these zeros into factors of the polynomial and multiplying them out.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F180e35fb-9b09-4fc5-8a6a-511bee286828%2F75f7fc3e-0197-43f0-b847-3ab5201e69a3%2F5jqphwa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Simplification and Zero-Finding
#### Exercise 1: Simplify by Multiplying
\[ (x + 6i)(x - 6i) \]
In this problem, we need to simplify the expression by multiplying the two binomials.
#### Exercise 2: Finding a Polynomial with a Given Zero
\[ \text{Find a polynomial with zero } x = 4i. \]
In this problem, we need to find a polynomial such that \( x = 4i \) is one of its zeros.
Note: In the second exercise, some text is unreadable due to a scribble, but the instruction is clear about finding a polynomial with a specified zero.
### Steps for Exercise 1:
1. Distribute the terms in the binomials.
2. Apply the difference of squares formula where applicable.
3. Simplify the resulting expression.
### Steps for Exercise 2:
1. Use the fact that for a polynomial to have a non-real zero \( x = 4i \), the conjugate \( x = -4i \) must also be a zero.
2. Formulate the polynomial by combining these zeros into factors of the polynomial and multiplying them out.
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 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.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,
