how to solve

HW 2.2.1: Complex Roots Visualization Consider the graph of f (x)= x' -4x+5 a. Graph f (x) in detail in the xy plane of the coordinate system provided on the nex page without using a graphing calculator. f ( ) = 47- 4 x 45 b. What conclusion can you make about the roots of f(x) ? ( (* ) =(x2-4x+4)+ = (-2)721 c. Show that 2-/ is a root for f(x) - 4-4 4- 8 THTAS "2 = 12 ( R1) 192 1' 4+ 1-815 d. Show that f (2-3/) is a real number. e. Show that f (3+7) is not a real number. f. Try a few more complex values and make a conjecture about values of a and b fo 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 X