Let f=z" + an-12¹-1 + ... + a₁ € C[z] be a polynomial of degree n ≥ 1. Which of the factorisations below must exist? Select one or more: a. f=(z-C₁)(z-C₂)(z- Cn), where C₁, ..., Cn are complex numbers b. f= (z-C₁)(z-C₂)(z-Cn), where C₁, . ...., Cn are different complex numbers c. f=g₁(z) gk(z), where g₁, . ...., 9k € C[z] each have exactly one root, and all these roots are different d. f = (z² + r₁Z+S₁)... (z² + rkz + Sk), where r₁, ..., rk and S₁, ..., Sk are real numbers e. f=g₁(z) gk(z), where g₁, , ..., 9k € C[z] each have exactly one root, and their degrees are all different
Let f=z" + an-12¹-1 + ... + a₁ € C[z] be a polynomial of degree n ≥ 1. Which of the factorisations below must exist? Select one or more: a. f=(z-C₁)(z-C₂)(z- Cn), where C₁, ..., Cn are complex numbers b. f= (z-C₁)(z-C₂)(z-Cn), where C₁, . ...., Cn are different complex numbers c. f=g₁(z) gk(z), where g₁, . ...., 9k € C[z] each have exactly one root, and all these roots are different d. f = (z² + r₁Z+S₁)... (z² + rkz + Sk), where r₁, ..., rk and S₁, ..., Sk are real numbers e. f=g₁(z) gk(z), where g₁, , ..., 9k € C[z] each have exactly one root, and their degrees are all different
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let f=z" + an-12¹-1 + ... + a₁ € C[z] be a polynomial of degree n ≥ 1. Which of the factorisations
below must exist?
Select one or more:
a. f=(z-C₁)(z-C₂)(z- Cn), where C₁, ..., Cn are complex numbers
b.
f= (z-C₁)(z-C₂)(z-Cn),
where C₁, .
...., Cn are different complex numbers
c. f=g₁(z) gk(z), where g₁, .
...., 9k € C[z] each have exactly one root, and all these roots
are different
d.
f = (z² + r₁Z+S₁)... (z² + rkz + Sk), where r₁, ..., rk and S₁, ..., Sk are real numbers
e. f=g₁(z) gk(z), where g₁, , ..., 9k € C[z] each have exactly one root, and their degrees
are all different](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F283b3a0d-0821-472c-a1ce-fcf162c3f2c6%2Fed35d2d8-36da-4bb2-a412-75fef09aa1ce%2F656fo4d_processed.png&w=3840&q=75)
Transcribed Image Text:Let f=z" + an-12¹-1 + ... + a₁ € C[z] be a polynomial of degree n ≥ 1. Which of the factorisations
below must exist?
Select one or more:
a. f=(z-C₁)(z-C₂)(z- Cn), where C₁, ..., Cn are complex numbers
b.
f= (z-C₁)(z-C₂)(z-Cn),
where C₁, .
...., Cn are different complex numbers
c. f=g₁(z) gk(z), where g₁, .
...., 9k € C[z] each have exactly one root, and all these roots
are different
d.
f = (z² + r₁Z+S₁)... (z² + rkz + Sk), where r₁, ..., rk and S₁, ..., Sk are real numbers
e. f=g₁(z) gk(z), where g₁, , ..., 9k € C[z] each have exactly one root, and their degrees
are all different
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