Answers for Lesson 5–8   Exercises

1.	1, 3                             2. –6, –2	        3.  1
4.	–1,                            5. –5           	               6.  1
7.                  8. –3                           9. 
10.                  11. 1, 4	         12. 
13. 3i                  14. 12i	                 15. 
16. –2i                17. 1                  18. 
19.              20.              21. 
22.  3                         	          23.  0.61, 2.72
24. –1.87, 0.54       	          25. 1
26. –1.24, 1.38      		27. –2.49, 0.89
28. –2.90, 1.90     	 	29.  –0.19, 2.69
30. –0.81, 0.31                   31.	 –4; two, imaginary
32. 36; two, real                                   33. 0; one, real
34. –223; two, imaginary                    35.	169; two, real
36. –116; two, imaginary                    37. 1; two, real
38. 0; one, real             39. 0; one, real            40.  no
41. 1, 10                         42. 0, 42	                 43. 
44. –3.45, 1.45              45. 1 i                          46. –1.70, 4.70
47. –7, 7                         48. –8.47, 0.47	            49. 3 i

50.                   51. –1, 6	                    52. –5.41, 2.41

Answers for Lesson 5–8   Exercises (cont.)

53.	a. w(18 – w) = 36
b. 2.29 in. by 15.71 in.
54.	3 or –
55.	Answers may vary. Sample: Assume the coefficients are real numbers. If the discriminant is negative, then there are 2 imaginary solutions. If the discriminant is 0, then there is 1 
real solution. If the discriminant is positive, then there are 2 
real solutions.
56.	a.  Answers may vary. Sample:
Graph y = 0.0721x2 – 2.8867x + 117.061 and y = 100. Where they intersect is the year when 100 million tons were released in the air.
Wherever y = 0.0721x2  – 2.8867x + 117.061 is below 
y = 100 is where less than 100 million tons were released.
b.	Answers may vary. Sample:
Where y = 0.0721x2 – 2.8867x + 117.061 < 100 is the solution. Subtract 100 from both sides and you get 
y = 0.0721x2 – 2.8867x + 17.061 < 0. You then use the quadratic formula to solve.
c.	Check students’ work.
57.	 two	58.  one	59.  none
60.  two                       61.  two                        62.  two
63.	a. 12 or –12
b.	k such that < 12
c.	k such that  > 12
64.	a. k such that  < 6
b.	k such that  > 6
c.	6, –6

Answers for Lesson 5-8    Exercises (cont.)

65.	Imaginary solutions always come in pairs because they are the positive and negative solutions of the square root of a negative number.
66.	a.  II
b.	 III
c.	 I
67.	a. x2 = 100
b.  17.72 cm

68. a. yes
c. 0 < t < 5

69. Answers may vary. Sample: x2	– 3x + 1 = 0
70. Answers may vary. Sample: x2 + 5x + 3 = 0
71. Answers may vary. Sample: x2	– 5x + 7 = 0
72.              73.           74. –a 
75. a. b.