C H A P T E R 2 Polynomial and Rational Functions

79.
Let fx x4 gx 5x
2.
5 10x 5xx4 2
81.
83.
Sign variations: 0, positive zeros: 0
fx x 4 2
Sign variations: 0, negative zeros: 0
hx 3x 4 2x 2 1
Sign variations: 0, positive zeros: 0
hx 3x 4 2x 2 1
Sign variations: 0, negative zeros: 0
gx 2x 3 3x 2 3
Sign variations: 1, positive zeros: 1
gx 2x 3 3x 2 3
Sign variations: 0, negative zeros: 0
85. fx 5x3 x2 x 5
Sign variations: 3, positive zeros: 3 or 1
fx 5x 3 x 2 x 5
Sign variations: 0, negative zeros: 0
1 is a lower bound.
80.
82.
84.
86.
Section 2.5 Zeros of Polynomial Functions 199
hx 4x 2 8x 3
Sign variations: 2, positive zeros: 2 or 0
hx 4x 2 8x 3
Sign variations: 0, negative zeros: 0
hx 2x 4 3x 2
Sign variations: 2, positive zeros: 2 or 0
hx 2x 4 3x 2
Sign variations: 0, negative zeros: 0
f x 4x 3 3x 2 2x 1
Sign variations: 3, positive zeros: 3 or 1
f x 4x 3 3x 2 2x 1
Sign variations: 0, negative zeros: 0
f x 3x 3 2x 2 x 3
Sign variations: 0, positive zeros: 0
f x 3x 3 2x 2 x 3
Sign variations: 3, negative zeros: 3 or 1
87. fx x
(a) 4 1 4 0 0 15
4 0 0 0
1 0 0 0 15
4 is an upper bound.
(b) 1 1 4 0 0 15
1 5 5 5
1 5 5 5 20
4 4x3 15 88. fx 2x
(a) 4 2 3 12 8
8 20 32
2 5 8 40
4 is an upper bound.
(b) 3 2 3 12 8
6 27 45
2 9 15 37
3 3x 2 12x 8
3 is a lower bound.
3 is a lower bound.
89. fx x
(a) 5 1 4 0 16 16
5 5 25 205
1 1 5 41 189
5 is an upper bound.
(b) 3 1 4 0 16 16
3 21 63 141
1 7 21 47 125
4 4x3 16x 16 90. f x 2x
(a) 3 2 0 0
6 18
2 6 18
3 is an upper bound.
(b) 4 2 0
8
2 8
4 8x 3
3 is a lower bound.
8
54
46
0
32
32
3
138
141
8
128
136
3
544
547