M125 (Intermediate Algebra, Spring 2016-hybrid)
Test (11.3-11.5)
Name:
Use the discriminant to determine whether the following equations have solutions that are: two different rational
solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
1) w2 - 3w + 8 = 0
1)
A) Two different irrational solutions
C) Exactly one rational solution
B) Two different imaginary solutions
D) Two different rational solutions
2) 16x2 - 8x + 1 = 0
A) Two different rational solutions
C) Two different irrational solutions
B) Exactly one rational solution
D) Two different imaginary solutions
3) 3 - 4a 2 = 6a + 4
A) Two different imaginary solutions
C) Exactly one rational solution
B) Two different rational solutions
D) Two different irrational solutions
Write a quadratic equation having the given numbers as solutions.
7
1
4) , 3
2
A) 6x2 - 11x - 7 = 0
C) 6x2 + 11x - 7 = 0
5) 4, only solution
A) x2 + 4x + 16 = 0
B) x2 - 8x + 16 = 0
C) x2 - 16 = 0
3,4+ 3
A) x2 - 8x + 3x + 13 = 0
C) x2 - 4x + 13 = 0
A) x2 + 4 = 0
3)
4)
B) 6x2 + 6x - 7 = 0
D) 6x2 - 7x + 6 = 0
6) 4 -
7) 2i, -2i
2)
D) x2 + 8x + 16 = 0
5)
6)
B) x2 - 8x + 16 = 0
D) x2 - 8x + 13 = 0
B) x2 + 4i = 0
C) x2 - 4 = 0
D) x2 - 4ix + 4 = 0
Solve the problem.
8) Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer
than Juanita to do the job alone. How long would it take Juanita alone?
A) 3 hr
B) 6 hr
C) 15 hr
D) 9 hr
7)
8)
9) Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than
the other to fill the tank. How long would each pipe take to fill the tank alone?
A) 25 hr for one
B) 10 hr for one
50 hr for the other
20 hr for the other
C) 15 hr for one
D) 12.5 hr for one
30 hr for the other
25 hr for the other
9)
10) Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than
the rate going, and if the distance each way was 7 miles, find her rate going.
A) 3.7 mph
B) 5.9 mph
C) 1.5 mph
D) 5.5 mph
10)
1
11) Amy travels 450 miles at a certain speed. If the car had gone 15 mph faster, the trip would have
taken 1 hour less. Find Amy's speed.
A) 72 mph
B) 75 mph
C) 68 mph
D) 78 mph
11)
12) 7m -2 + 4m -1 - 3 = 0
7
A) , - 1
3
3
B) - , 1
7
3
C) , -1
7
12)
13) 6x2/5 + 8x1/5 + 2 = 0
1
A) - 1, 3
1
B) 1,
243
1
C) - 1, 243
Solve.
14) x4 - 12x2 + 27 = 0
A) ±3, ±2 3
13)
D) 2, 3
14)
B) ±3, ± 3
C) 3,
Find the x-intercepts of the graph of the function.
15) f(x) = x1/2 + 3x1/4 - 4
A) (1, 0), (256, 0)
7
D) - , 1
3
B) (1, 0), (-4, 0)
3
C) (4, 0)
2
D) ±3, ±3
D) (1, 0)
15)
Answer Key
Testname: PRAC8(11.3_11.5)
1) B
2) B
3) D
4) A
5) B
6) D
7) A
8) D
9) C
10) B
11) B
12) A
13) C
14) B
15) D
3