Name: __________________
1 A partial solution set
x
3
+ 6x
2
(4)
Class:
Date: _____________
is given for the equation
15x 100 = 0
Find the complete solution set.
2 A partial solution set
x
3
+ 9x
2
( 3)
is given for the equation
+ 11x 21 = 0
Find the complete solution set.
3 A partial solution set
x
4
4x
3
11x
( 2, 2 )
2
is given for the equation
+ 60x 60 = 0
Find the complete solution set.
4 A partial solution set
x
4
10x
3
( 6,4 )
+ 25x
2
is given for the equation
10x + 24 = 0
Find the complete solution set.
5 Find a polynomial with the zeros (7 , 3).
6 Find a polynomial with the zeros (6 , 5 , 1).
7 Find a polynomial with the zeros
(
8 Find a polynomial with the zeros
( 0,0,0,
2 ,
9 Find a polynomial with the zeros
(i,
).
10 Find a polynomial with the zeros
PAGE 1
1,5,
6 , i
7, 7
).
2
( 0,2 i,2 + i )
).
.
Name: __________________
Class:
Date: _____________
11 Use synthetic division to express
P (x) = 5x
3
30x
2
32x 37
in the form (divisor)(quotient) + remainder for the divisor
x 7
12 Use synthetic division to express
P(x) = 5x
3
+ 14x
2
22x + 28
in the form (divisor)(quotient) + remainder for the divisor
13 Use synthetic division to do the division
2x
3
2
+ 3x + 18x 23
x 1
14 Use synthetic division to do the division
3x
3
2
7x 5x + 29
x + 1
15 Use synthetic division to do the division
2x
4
PAGE 2
3
2x 91x + 4
x 4
x + 4
Name: __________________
Class:
16 Use synthetic division to do the division
3x
5
7203x
x 7
17 Let
P(x) = 5x
3
+ 2x
2
5x + 6
Use synthetic division to find the value P( 5 )
18 Let
P(x) = 3x
4
7x
2
+ 5
Use synthetic division to find the value P( 5i )
19 Let
P(x) = x
4
10x
3
+ 4x + 6x
2
7
Write the terms of P(x) in descending powers of x
20 Let
2
P(x) = 3 4x + 4x
5
5x
3
Use synthetic division to find the value P( 2i )
21 Tell how many roots the equation has.
2
x =3
22 Tell how many roots the following has
15
7x
PAGE 3
6x13 4x = 3
Date: _____________
Name: __________________
Class:
Date: _____________
23 Tell how many roots the equation has
x104 x4 = 1
24 One root of the equation
x (7x 6) = 5x
6
is 0. How many other roots are there?
25 One root of the equation
5x (x 9x + 7) = 0
2
7
is 0. How many other roots are there?
26 Write a third degree polynomial equation with real coefficients and the roots 4 , i.
27 Write a third degree polynomial equation with real coefficients and the roots 2 , i.
28 Write a third degree polynomial equation with real coefficients and the roots 3 , 3 + i.
29 Write a third degree polynomial equation with real coefficients and the roots 8 i , 1.
30 Write a fourth degree polynomial equation with real coefficients and the roots 3, 5, i.
31 Write a fourth degree polynomial equation with real coefficients and the roots 1 , 4 , 2 + i.
32 Write a fourth degree polynomial equation with real coefficients and the roots
i , 1 i.
33 Find integer bounds for the roots of the equation
x 2x 9 = 0
2
34 Find integer bounds for the roots of the equation
6x 13x 110x = 0
3
PAGE 4
2
Name: __________________
35 Find integer bounds for the roots of the equation
3x 11x 2x
5
4
3
+ 38x 21x 15 = 0
2
36 Find all rational roots of the equation.
x 5x x + 5 = 0
2
3
37 Find all rational roots of the equation.
x 3x 9x + 27 = 0
3
2
38 Find all rational roots of the equation.
x + 5x x 5 = 0
3
2
39 Find all rational roots of the equation.
x 13x + 56x 92x + 48 = 0
4
3
2
40 Find all rational roots of the equation.
4
3
2
x + 8x + 24x + 32x + 16 = 0
41 Find all rational roots of the equation.
x 9x + 17x + 9x 18 = 0
3
4
2
42 Find all rational roots of the equation.
x 2x 10x + 20x + 9x 18 = 0
5
4
3
2
43 Find all rational roots of the equation.
x 48x + 768x 4096x = 0
5
7
3
44 Find all rational roots of the equation.
75x 50x + 27x 18 = 0
2
3
45 Find all rational roots of the equation.
20x + 76x 111x + 44x 5 = 0
4
3
2
46 Find all rational roots of the equation.
26x 15x + 27x 15x + 1 = 0
4
3
2
47 Find all rational roots of the equation.
7x 3x + 28x 12 = 0
3
PAGE 5
2
Class:
Date: _____________
Name: __________________
Class:
48 Find all rational roots of the equation.
7x 2x + 7x 2 = 0
2
3
49 The number (1 + i) is a root of the equation.
x 11x + 20x 18 = 0
3
2
Find the other roots of the equation.
50 The number (1 + i) is a root of the equation.
x 2x 47x
3
4
2
+ 98x 98 = 0
Find the other roots of the equation.
51 The number (1 + i) is a root of the equation.
x 2x 47x
3
4
2
+ 98x 98 = 0
Find the other roots of the equation.
52 The number (1 + i) is a root of the equation.
x 2x 79x + 162x 162 = 0
4
3
2
Find the other roots of the equation.
53 Solve the equation.
x
3
32 x 2 + 92 x 16 = 0
3
3
54 Find all rational roots of the equation.
1
1 5x
10x 2 + 50x 3 + 9x 4 45x 5 = 0
55 Find all rational roots of the equation.
1
1 16x
2
+ 91x
216x 3 + 180x 4 = 0
56 Find the positive root of the equation using the bisection method.
x
2
3 = 0
57 Find the negative root of the equation using the bisection method.
x
2
2 = 0
58 Find the positive root of the equation using the bisection method.
x
2
13 = 0
PAGE 6
Date: _____________
Name: __________________
Class:
Date: _____________
59 Find the negative root of the equation using the bisection method.
x
2
10 = 0
60 Find the positive root of the equation using the bisection method.
x
3
x
2
3 = 0
61 Find the negative root of the equation using the bisection method.
x
3
x + 3 = 0 ,
62 Find the negative root of the equation using the bisection method.
3x
4
+ 3x
3
x
2
4x 5 = 0 ,
63 Find the positive root of the equation using the bisection method.
x
5
+ x
4
4x
3
4x
2
5x 5 = 0
64 Use a graphing calculator to find the distinct real solutions of the equation.
x
2
5 = 0
65 Use a graphing calculator to find the real solution of the equation.
x
2
2x + 1 = 0
66 Use a graphing calculator to find the distinct real solutions of the equation.
x
3
7x
2
+ 15x 9 = 0
67 Use a graphing calculator to find the real solutions of the equation.
x
3
3x
PAGE 7
2
8x + 24 = 0
Name: __________________
68
Class:
Date: _____________
3
Use the bisection method or a graphing calculator to find the coordinates of the two points on the graph of y = x that lie r = 1 unit from the
origin. Give the result to the nearest hundredth.
69 The length of the shipping crate is to be 2 feet greater than its height and 5 feet greater than its width, and its volume is to be 170 cubic feet. Use
the bisection method or a graphing calculator to find the height of the crate to the nearest tenth of a foot.
PAGE 8
ANSWER KEY
Name: __________________
Class:
Date: _____________
1.
4, 5, 5
24. 6
47.
2.
1, 3, 7
25. 8
48.
3.
2,2, 15,
26. x3 4x2+x 4=0
49.
4.
6,4, i,i
27. x3 2x2+x 2=0
50.
5.
x 10x+21
28. x3 9x2+28x 30=0
51.
6.
x 12x +41x 30
29. x3 15x2+49x+65=0
52.
7.
x 4x 12x +28x+35
30. x4 8x3+16x2 8x+15=0
53.
8.
x 2x
9.
x
15
2
3
2
4
3
5
3
3
2
4
2
6 x +x
6
10. x3 4x2+5x
3
3
7
2
7
9,1 i
7, 7,1 i
7,1 i
7, 7,1 i,1+i
7, 7,1 i
7,1 i,1+i
7,1 i
7, 7,1 i
7,1 i
7, 7,1 i,1+i
7, 7,1 i
7,1 i,1+i
7,1 i
9, 9,1 i
2 ,6,4
3
2
31. x 9x +29x 41x+20=0
54. 1,3, 1, 3,5
32. x4 2x3+3x2 2x+2=0
55. 2,5,3,6
33. 2,5
56.
1.7
x=1.7
1.4
x= 1.4
11.
( x 7) ( 5x +5x+3) 16
2
( x 7) ( 5x +5x+3) 16
34. 4,6
57.
12.
( x+4 ) ( 5x 6x+2 ) +20
35. 2,4
58.
36. 1, 1,5
59.
37. 3, 3,3
60.
38. 1, 1, 5
61.
16. 3x +21x +147x +1029x
39. 2,4,1,6
62.
17. 656
40. 2, 2, 2, 2
63.
18. 2055
41. 1,6, 1,3
64.
19. x4 10x3+6x2+4x 7
42. 1,3, 1, 3,2
65.
20. 19+168i
43. 0,4,4,4, 4, 4, 4
66.
21. 2
2
44.
3
67. 2.8, 2.8,3.0
2
2
13. 2x2+5x+23
2
14. 3x 10x+5+
3
24
x+1
2
15. 2x +6x +24x+5+
4
PAGE 1
3
24
x 4
2
3.6
x=3.6
3.2
x= 3.2
1.9
x=1.9
1.7
x= 1.7
1.3
x= 1.3
2.2
x=2.2
2.2, 2.2
1
x=1
1,3
ANSWER KEY
Name: __________________
22. 15
23. 104
PAGE 2
Class:
1 , 1 , 5, 1
2 2
5
1, 1
46.
2 13
45.
Date: _____________
68.
( 0.83,0.56 ) , ( 0.83, 0.56 )
69. 6.3