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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 41RE
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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.
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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