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

69.
71.
73.
gx x 4 4x 3 8x 2 16x 16
Possible rational zeros: ±1, ±2, ±4, ±8, ±16
2 1
1
2 1
1
4
2
2
2
2
0
8
4
4
4
0
4
8
8
0
16
8
8
gx x 2x 2x 2 4 x 2 2 x 2ix 2i
The zeros of gx are 2 and ±2i.
fx x 4 10x 2 9
x 2 1x 2 9
16
16
0
x ix ix 3ix 3i
The zeros of fx are x ±i and x ±3i.
fx x 3 24x 2 214x 740 74.
Possible rational zeros:
Based on the graph, try x 10.
By the Quadratic Formula, the zeros of x are
2 14x 74
x
−20
10 1
1
2000
−1000
24
10
14
14 ± 196 296
2
±1, ±2, ±4, ±5, ±10, ±20, ±37,
±74, ±148, ±185, ±370, ±740
The zeros of fx are x 10 and x 7 ± 5i.
10
214
140
74
740
740
0
7 ± 5i.
Section 2.5 Zeros of Polynomial Functions 197
70. hx x
Possible rational zeros: ±1, ±3, ±9
4 6x 3 10x 2 6x 9
72.
3 1
1
3 1
1
6
3
3
3
3
0
10
9
1
0
The zeros of x are x ±i.
2 1
Zeros:
hx x 3 2 x 3, ±i
x ix i
1
Zeros: x ±2i, ±5i
1
6
3
3
3
f x x 4 29x 2 100
x 2 25x 2 4
0
3
9
9
f x x 2ix 2ix 5ix 5i
f s 2s 3 5s 2 12s 5
Possible rational zeros:
Based on the graph, try
1
2
By the Quadratic Formula, the zeros of 2s are
2 2s 5
s
2
2
10
−10 10
−10
5
1
4
12
2
10
2 ± 4 20
2
5
5
0
s 1
2 .
1 ± 2i.
The zeros of are s 1
and s 1 ± 2i.
fs
2
0
±1, ±5, ± 1 5
2 , ± 2