5. Choose 21, 22, 23 E C such that Re(21) = 0 Im(2₁) 0 Re(22) 0 Im(2₂) = 0 Re(23)0 Im(23) ‡ 0 Consider the cubic function f(x) with roots z₁, 22 and 23. (a) Give an equation for f(x). (b) Find complex numbers uo, u₁, u2 and u3 such that ƒ(x) = U3x³ + U2x² + u₁x¹ + uo (Check your work here.) Part a) should be quick. Part b) will be tedious. A few tedious problems are helpful for improving your skills with complex numbers. Another intent of this problem is for you to think about the Fundamental Theorem of Algebra.
5. Choose 21, 22, 23 E C such that Re(21) = 0 Im(2₁) 0 Re(22) 0 Im(2₂) = 0 Re(23)0 Im(23) ‡ 0 Consider the cubic function f(x) with roots z₁, 22 and 23. (a) Give an equation for f(x). (b) Find complex numbers uo, u₁, u2 and u3 such that ƒ(x) = U3x³ + U2x² + u₁x¹ + uo (Check your work here.) Part a) should be quick. Part b) will be tedious. A few tedious problems are helpful for improving your skills with complex numbers. Another intent of this problem is for you to think about the Fundamental Theorem of Algebra.
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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Transcribed Image Text:5. Choose 21, 22, 23 E C such that
Re(21) = 0
Im(2₁) 0
Re(22) 0
Im(2₂) = 0
Re(23)0 Im(23) ‡ 0
Consider the cubic function f(x) with roots z₁, 22 and 23.
(a) Give an equation for f(x).
(b) Find complex numbers uo, u₁, u2 and u3 such that
ƒ(x) = U3x³ + U2x² + u₁x¹ + uo
(Check your work here.)
Part a) should be quick. Part b) will be tedious. A few tedious problems are helpful for
improving your skills with complex numbers. Another intent of this problem is for you to
think about the Fundamental Theorem of Algebra.
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