Download Quadratic Equations

Intermediate Algebra
Quadratic Equations
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the zero-factor property to solve the equation.
1) x2 + 7x + 6 = 0
A) {0, 6}
2) 2x2 + x - 15 = 0
5
A) -3,
2
3) x2 = 10x - 24
A) {4, 6}
B) {-6, 0}
C) {-6, -1}
5
2
B) -3, -
C)
B) {-4, -6}
A) {7, -7}
D) {1, 6}
5
,3
2
D) -
C) {-24, -1}
Use the square root property to solve the equation.
4) x2 = 49
B) {24.5}
1)
5
,3
2
3)
D) {1, 24}
C) {8, -8}
4)
D) {7}
5) x2 - 4 = 0
A) {2}
B) {2, -2}
C) {4.5}
D) {1, -1}
6) (x + 4)2 = 25
A) {-29}
B) {-9, 1}
C) {9, -1}
D) {1}
7) (3s + 8)2 = 36
2
14
A) - , 3
3
2
B) - , 0
3
2 14
,
C)
3 3
28
D)
3
C) {-7, -3}
D) {5, - 5}
Solve the equation by completing the square.
8) a2 - 10a + 21 = 0
A) {18, 3}
B) {7, 3}
9) z2 + 16z + 44 = 0
A) 8 + 2 5
C) -16 + 2 11
10) 0.1x2 - 0.2x - 0.5 = 0
A) {1 + 6, 1 - 6}
5)
6)
7)
8)
9)
B) 8 + 2 11, 8 - 2 11
D) -8 + 2 5, -8 - 2 5
10)
B) {2 -
6}
C) {2 +
Find the nonreal complex solutions of the equation.
11) x2 - 4x + 20 = 0
A) {2 + 4i, 2 - 4i}
2)
B) {6, -2}
6, 2 -
C) {4 + 8i, 4 - 8i}
1
6}
D) {1 +
6}
D) {-2 + 4i, -2 - 4i}
11)
12) x2 + 4x + 53 = 0
A) {-2 + 7i, -2 - 7i}
C) {2 + 7i, 2 - 7i}
12)
B) {5, -9}
D) {-2 + 53i, -2 -
53i}
Use the quadratic formula to solve the equation. (All solutions are real numbers.)
13) 2n 2 = -10n - 7
-10 + 11 -10 - 11
,
A)
2
2
C)
14)
13)
-5 + 39 -5 - 39
,
B)
2
2
-5 + 11 -5 - 11
,
2
2
D)
-5 + 11 -5 - 11
,
4
4
z2 z 5
= +
3
2 6
A)
14)
5
2
B) -1,
C) {-1}
D)
5
2
3 + 2 10 3 - 2 10
,
4
4
Use the quadratic formula to solve the equation.
15) x2 + x + 4 = 0
15)
A)
1 + i 15 1 - i 15
,
2
2
B)
C)
-1 + i 15 -1 - i 15
,
2
2
D)
16) 8x2 + 7x = -2
7 + i 15 7 - i 15
,
A)
16
16
C)
1+
2
15 1 ,
2
15
-1 + 15 -1 - 15
,
2
2
16)
-7 + i 15 -7 - i 15
,
16
16
B)
-7 + 15 -7 - 15
,
16
16
D)
7 + 15 7 - 15
,
16
16
Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational
solutions, or two nonreal complex solutions. Do not actually solve.
17) s2 + 3s - 4 = 0
17)
A) Two nonreal complex solutions
C) Two irrational solutions
B) One rational solution
D) Two rational solutions
18) t2 + 8t + 16 = 0
A) Two irrational solutions
C) Two rational solutions
B) One rational solution
D) Two nonreal complex solutions
19) 4y2 = 6y - 7
A) Two irrational solutions
C) Two nonreal complex solutions
B) One rational solution
D) Two rational solutions
2
18)
19)