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1. Consider the graph of f(x)=x² -4x+5 a. Graph f(x) in detail in the xy plane of the coordinate system provided on the next page without using a graphing calculator. b. What conclusion can you make about the roots of f(x)? C. Show that 2-i is a root for f(x). d. Show that f(2-3i) is a real number. e. Show that f(3+i) is not a real number.

1. Consider the graph of f(x)=x² -4x+5 a. Graph f(x) in detail in the xy plane of the coordinate system provided on the next page without using a graphing calculator. b. What conclusion can you make about the roots of f(x)? C. Show that 2-i is a root for f(x). d. Show that f(2-3i) is a real number. e. Show that f(3+i) is not a real number.

Advanced Engineering Mathematics
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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1. Consider the graph of f(x)=x² – 4x +5 a. Graph f(x) in detail in the xy plane of the coordinate system provided on the next page without using a graphing calculator. b. What conclusion can you make about the roots of f(x)? C. Show that 2-i is a root for f(x). d. Show that f(2-3i) is a real number. e. Show that f(3+i) is not a real number. f. Try a few more complex values and make a conjecture about values of a and b for which f(a+bi) is a real number. Explain how you arrived at your conjecture and prove that it is true. g. Lastly, draw a graphical representation of what your above answer implies about the real-valued outputs of fwith regard to the inclusion of a complex domain. y
Transcribed Image Text:1. Consider the graph of f(x)=x² – 4x +5 a. Graph f(x) in detail in the xy plane of the coordinate system provided on the next page without using a graphing calculator. b. What conclusion can you make about the roots of f(x)? C. Show that 2-i is a root for f(x). d. Show that f(2-3i) is a real number. e. Show that f(3+i) is not a real number. f. Try a few more complex values and make a conjecture about values of a and b for which f(a+bi) is a real number. Explain how you arrived at your conjecture and prove that it is true. g. Lastly, draw a graphical representation of what your above answer implies about the real-valued outputs of fwith regard to the inclusion of a complex domain. y
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