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

196 Chapter 2 Polynomial and Rational Functions
64.
65.
67.
f x x 3 2x 2 11x 52
Possible rational zeros: ±1, ±2, ±4, ±13, ±26
4 1
hx x 3 x 6
Possible rational zeros:
2 1
By the Quadratic Formula, the zeros of x are
2 2x 3
x
1
0
2
2
2 ± 4 12
2
1
4
3
±1, ±2, ±3, ±6
6
6
0
1 ± 2 i.
The zeros of hx are x 2 and x 1 ± 2 i.
hx x 2x 1 2 i x 1 2 i
x 2x 1 2 ix 1 2 i
fx 5x 3 9x 2 28x 6
Possible rational zeros:
±1, ±2, ±3, ±6, ± 1 2 3 6
5 , ± 5 , ± 5 , ± 5
1
5
By the Quadratic Formula, the zeros of
5x are
2 10x 30 5x2 2x 6
x
5
5
1
2
4
6
9
1
10
11
24
2 ± 4 24
2
13
28
2
30
52
52
By the Quadratic Formula, the zeros of x are x 2 6x 13
Zeros: x 4, 3 ± 2i
f x x 4x 3 2ix 3 2i
0
6
6
0
1 ± 5 i.
The zeros of are
fx x
5x 1x 1 5 ix 1 5 i
1
x
55x 1 5 i x 1 5 i
1
5 and x 1 ± 5 i.
fx
6 ± 36 52
2
66. hx x
Possible rational zeros: ±1, ±5, ±7, ±35
3 9x2 27x 35
By the Quadratic Formula, the zeros of x
4 ± 16 28
are x 2 ± 3i.
2
Zeros: 5, 2 ± 3i
hx x 5x 2 3ix 2 3i
2 5 1 9 27 35
5 20 35
1 4 7 0
4x 7
68. gx 3x 3 4x 2 8x 8
Possible rational zeros:
±1, ±2, ±4, ±8, ± 1 2 4 8
3 , ± 3 , ± 3 , ± 3
2
3
By the Quadratic Formula, the zeros of
3x are
2 6x 12 3x2 2x 4
x
3
3
3 ± 2i.
4
2
6
2 ± 4 16
2
8
4
12
8
8
0
1 ± 3i.
Zeros: x
gx 3x 2x 1 3ix 1 3i
2
3 , 1 ± 3i