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

142.
144.
146.
148.
12x 3 20x 2 < 0 143.
4x 2 3x 5 < 0
Critical numbers:
Test intervals:
x 0, x 5
3
, 0 ⇒ 12x 3 20x 2 < 0
Solution interval: , 0 0, 5
3
5
3 , ⇒ 12x3 20x2 0,
> 0
5
3 ⇒ 12x3 20x2 < 0
x 5
< 0 145.
3 x
Critical numbers:
x 5, x 3
Test intervals: , 3 ⇒
3, 5 ⇒
5, ⇒
x 5
< 0
3 x
x 5
> 0
3 x
x 5
< 0
3 x
Solution intervals: , 3 5,
1 1
>
x 2 x
1 1
> 0
x 2 x
Critical numbers:
Test intervals:
x 2, x 0
, 0 ⇒ 1 1
> 0
x 2 x
0, 2 ⇒ 1 1
< 0
x 2 x
2, ⇒ 1 1
> 0
x 2 x
Solution interval: , 0 2,
P
2000 ≤
10001 3t
5 t
10001 3t
5 t
20005 t ≤ 10001 3t
10,000 2000t ≤ 1000 3000t
1000t ≤ 9000
t ≥ 9 days
147.
Review Exercises for Chapter 2 257
2x 1 3x 1
≤ 0
x 1x 1
2x 2 3x 3
≤ 0
x 1x 1)
x 5
≤ 0
x 1x 1
Critical numbers: x 5, x ±1
Test intervals: , 5, 5, 1, 1, 1, 1,
x 5
Test: Is
≤ 0?
x 1x 1
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 5, 1 1,
2
x 1 ≤
3
x 1
x 4x 3
≥ 0
x
Critical numbers: x 4, x 3, x 0
Test intervals: , 4, 4, 3, 3, 0, 0,
x 4x 3
Test: Is
≥ 0?
x
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 4, 3 0,
x2 7x 12
≥ 0
x
50001 r 2 > 5500
149. False. A fourth-degree polynomial
can have at most four zeros and
complex zeros occur in conjugate
pairs.
1 r 2 > 1.1
1 r > 1.0488
r > 0.0488
r > 4.9%
150. False. (See Exercise 123.)
The domain of
f x 1
x 2 1
is the set of all real numbers x.