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

192 Chapter 2 Polynomial and Rational Functions
40.
45.
f x x 2x 4 ix 4 i
x 2x 2 8x 17
x 3 10x 2 33x 34
Note: f x ax where a is
any real number, has the zeros 2, 4 ± i.
3 10x 2 33x 34
42. If 1 3i is a zero, so is its conjugate, 1 3i.
44.
f x x 5 2 x 1 3ix 1 3i
x 2 10x 25x 2 2x 4
x 4 8x 3 9x 2 10x 100
Note: f x ax where
a is any real number, has the zeros 5, 5, 1 ± 3i.
4 8x 3 9x 2 10x 100,
f x x 4 2x 3 3x 2 12x 18
x 4
2x 3
6x 2
x 2 2x 3
x 6 ) x 4 2x 3 3x 2 12x 18
x 4 2x 3 3x 2 12x 6
12x
3x2 3x
0
2 2x
18
3 3x2 18
f x x 4 4x 3 5x 2 2x 6
x 2 2x 2 ) x 4 4x 3 5x 2 2x 6
x 4 2x 3 2x 2
x 4 2x 3 7x 2 2x 6
2x 3 4x 2 4x
2x 3 3x 2 6x 6
3x 2 6x 6
3x 2 6x 0
fx x 2 2x 2x 2 2x 3
46. fx x4 3x3 x2 12x 20
x 2 2x 3
x2 4 ) x4 3x3 x2 x
12x 20
2 3x 5
x 4 4x 2
3x 3 5x 2 12x
3x 3 12x
5x2 5x
20
2 20
0
41. If is a zero, so is its conjugate,
3x2 x 2x 32 2i 2 3 2i
3 2i.
f x 3x 2x 1x 3 2ix 3 2i
3x 2x 1x 3 2ix 3 2i
3x 2 x 2x 2 6x 9 2
3x 2 x 2x 2 6x 11
3x 4 17x 3 25x 2 23x 22
Note: f x a3x where a is
2
any nonzero real number, has the zeros , 1, and 3 ±2i.
4 17x3 25x2 23x 22,
43.
(a)
(b) f x x
(c) f x x 3ix 3ix 3x 3
2 f x x
9x 3x 3
2 9x2 f x x
3
4 6x2 27
(a)
(b) f x x 6x 6x 2 f x x
2x 3
2 6x 2 2x 3
(c) f x x 6x 6x 1 2ix 1 2i
(a)
(b) fx x 1 3 x 1 3 x
(c) fx x 1 3 x 1 3 x 1 2 i x 1 2 i
Note: Use the Quadratic Formula for (b) and (c).
2 fx x
2x 3
2 2x 2x2 2x 3
(a)
(b)
f x x 2 4x 2 3x 5
f x x 2 3 29
4x
2
3 29
(c) f x x 2ix 2ix
2
3 29
x
2
3
3 29
x
2