Deck 8: Quadratic Functions

Question 1

Use the square root property to solve the equation.

- $$4 x ^ { 2 } = 28$$

A) $$\pm 7$$
B)14
C) $$\pm \sqrt { 7 }$$
D)8

Answer 1

$$\pm \sqrt { 7 }$$

Question 2

Use the square root property to solve the equation.

- $$3 x ^ { 2 } = 12$$

A) $$\pm 3$$
B) $$\pm 2$$
C)0
D) $$\pm 2 \sqrt { 3 }$$

Answer 2

$$\pm 2$$

Question 3

Solve the equation by completing the square.

- $$x ^ { 2 } = 3 - 8 x$$

A) $$- 1 \pm \sqrt { 19 }$$
B) $$- 4 \pm \sqrt { 19 }$$
C) $$4 + \sqrt { 19 }$$
D) $$- 4 \pm 2 \sqrt { 19 }$$

Answer 3

$$- 4 \pm \sqrt { 19 }$$

Question 4

Solve the equation by completing the square.

- $$x ^ { 2 } + 3 x - 9 = 0$$

A) $$\frac { - 3 - 3 \sqrt { 5 } } { 2 }$$
B) $$- 3 \pm 3 \sqrt { 5 }$$
C) $$\frac { 3 + 3 \sqrt { 5 } } { 2 }$$
D) $$\frac { - 3 \pm 3 \sqrt { 5 } } { 2 }$$

Question 5

Solve the equation by completing the square.

- $$x ^ { 2 } + 4 x = 7$$

A) $$- 1 \pm \sqrt { 11 }$$
B) $$- 2 \pm \sqrt { 11 }$$
C) $$2 + \sqrt { 11 }$$
D) $$- 2 \pm 2 \sqrt { 11 }$$

Question 6

Use the square root property to solve the equation.

- $$( 4 x + 3 ) ^ { 2 } = 10$$

A) $$\frac { - 3 \pm \sqrt { 10 } } { 4 }$$
B) $$\frac { \sqrt { 10 } \pm 3 } { 4 }$$
C) $$- \frac { 13 } { 4 } , \frac { 7 } { 4 }$$
D) $$\frac { 3 \pm \sqrt { 10 } } { 4 }$$

Question 7

Use the square root property to solve the equation.

- $$x ^ { 2 } + 36 = 0$$

A) $$\pm 6 \mathrm { i }$$
B)6
C) $$6 \mathrm { i }$$
D) $$\pm 6$$

Question 8

Use the square root property to solve the equation.

- $$7 x ^ { 2 } + 2 = 177$$

A)5
B)± 6
C)88.5
D) $$\pm 5$$

Question 9

Use the square root property to solve the equation.

- $$( 5 x + 5 ) ^ { 2 } = 100$$

A)1, 3
B)0, 1
C) $$\pm 21$$
D)-3, 1

Question 10

Solve the equation by completing the square.

- $$x ^ { 2 } - 12 x - 7 = 0$$

A) $$- 6 \pm \sqrt { 43 }$$
B) $$6 \pm \sqrt { 7 }$$
C) $$6 \pm \sqrt { 43 }$$
D) $$12 \pm \sqrt { 151 }$$

Question 11

Solve the equation by completing the square.

- $$x ^ { 2 } + 4 x - 9 = 0$$

A) $$- 2 \pm \sqrt { 13 }$$
B) $$- 1 \pm \sqrt { 13 }$$
C) $$2 + \sqrt { 13 }$$
D) $$- 2 \pm 2 \sqrt { 13 }$$

Question 12

Solve the equation by completing the square.

- $$5 x ^ { 2 } - 2 x - 5 = 0$$

A) $$\frac { - 1 \pm \sqrt { 26 } } { 5 }$$
B) $$- 5 , \frac { 27 } { 5 }$$
C) $$\frac { 1 \pm \sqrt { 26 } } { 5 }$$
D) $$\frac { 5 \pm \sqrt { 26 } } { 25 }$$

Question 13

Solve the equation by completing the square.

- $$x ^ { 2 } + 14 x + 30 = 0$$

A) $$- 7 \pm \sqrt { 19 }$$
B) $$7 \pm \sqrt { 30 }$$
C) $$7 + \sqrt { 19 }$$
D) $$- 14 + \sqrt { 30 }$$

Question 14

Use the square root property to solve the equation.

- $$( 3 x - 1 ) ^ { 2 } = \frac { 4 } { 9 }$$

A) $$- \frac { 2 } { 3 } , \frac { 2 } { 3 }$$
B)3, -1
C) $$- \frac { 2 } { 9 } , \frac { 2 } { 9 }$$
D) $$\frac { 5 } { 9 } , \frac { 1 } { 9 }$$

Question 15

Use the square root property to solve the equation.

- $$( 2 x - 3 ) ^ { 2 } = 49$$

A)-4, 10
B)-2, 5
C)-10, 4
D)-5, 2

Question 16

Use the square root property to solve the equation.

- $$( x - 5 ) ^ { 2 } = 16$$

A) $$\pm 4$$
B)21
C)1, 9
D) $$- 9,1$$

Question 17

Use the square root property to solve the equation.

- $$\left( x - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 9 } { 4 }$$

A)2, -1
B)1, -2
C)2, -4
D)4, -2

Question 18

Use the square root property to solve the equation.

- $$( 3 x - 4 ) ^ { 2 } = 8$$

A) $$\pm 2 \sqrt { 3 }$$
B) $$- \frac { 4 } { 3 } , 4$$
C) $$\frac { 4 \pm 2 \sqrt { 2 } } { 3 }$$
D) $$\frac { - 4 \pm 2 \sqrt { 2 } } { 3 }$$

Question 19

Use the square root property to solve the equation.

- $$\left( x + \frac { 4 } { 5 } \right) ^ { 2 } = \frac { 5 } { 25 }$$

A) $$\frac { \sqrt { 5 } \pm 4 } { 5 }$$
B) $$\frac { - 4 \pm \sqrt { 5 } } { 5 }$$
C) $$- \frac { 9 } { 5 } , \frac { 1 } { 5 }$$
D) $$\frac { 4 \pm \sqrt { 5 } } { 5 }$$

Question 20

Solve the equation by completing the square.

- $$x ^ { 2 } - 10 x + 21 = 0$$

A)3, 18
B) $$- 7 , - 3$$
C) $$\pm \sqrt { 21 }$$
D)3, 7

Question 21

Solve the equation by completing the square.

- $$2 x ^ { 2 } - \frac { 10 } { 3 } x + \frac { 2 } { 3 } = 0$$

A) $$\frac { - 5 \pm \sqrt { 13 } } { 6 }$$
B) $$\frac { 5 \pm \sqrt { 13 } } { 6 }$$
C) $$\frac { 10 \pm \sqrt { 13 } } { 6 }$$
D) $$\frac { - 10 \pm \sqrt { 13 } } { 12 }$$

Question 22

Solve the equation by completing the square.

- $$\frac { x ^ { 2 } } { 16 } + x + \frac { 21 } { 8 } = 0$$

A) $$8 + \sqrt { 22 }$$
B) $$- 16 \pm \sqrt { 42 }$$
C) $$- 8 \pm \sqrt { 22 }$$
D) $$8 - \sqrt { 42 } , 8 + \sqrt { 42 }$$

Question 23

Solve the equation by completing the square.

- $$3 x ^ { 2 } + 21 x = - 36$$

A) $$\pm \frac { 1 } { 2 }$$
B) $$- 4 , - 3$$
C) $$\pm \frac { 1 } { 2 } \mathrm { i }$$
D)3, 4

Question 24

Solve the problem.

-A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 228 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

A) $$3249 \mathrm {~ ft } ^ { 2 }$$
B) $$9747 ~\mathrm { ~ft } ^ { 2 }$$
C) $$6498 \mathrm { ~ft } ^ { 2 }$$
D) $$12,996 \mathrm { ~ft } ^ { 2 }$$

Question 25

Solve the equation by completing the square.

- $$x ^ { 2 } + x + 6 = 0$$

A) $$\frac { - 1 \pm \sqrt { 23 } } { 2 }$$
B) $$\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } i$$
C) $$- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$$
D) $$\frac { 1 \pm \sqrt { 23 } } { 2 }$$

Question 26

Solve the problem.
The length of a rectangular storage room is 7 feet longer than its width. If the area of the room is 120 square feet, find its dimensions.

A)w = 9 ft; l = 16 ft
B)w = 7 ft; l = 16 ft
C)w = 8 ft; l = 15 ft
D)w = 7 ft; l = 14 ft

Question 27

Solve the problem.

-The area of a circle is found by the equationon A $$\mathrm { A } = \pi \mathrm { r } ^ { 2 }.$$ . If Ifthe area A of a certain circle is 49? square centimeters, find its radius r.

A) $$\mathrm { r } = 7 \sqrt { \pi } \mathrm { cm }$$
B) $$\mathrm { r } = \pm 7 \mathrm {~cm}$$
C) $$\mathrm { r } = 7 \pi \mathrm { cm }$$
D) $$\mathrm { r } = 7 \mathrm {~cm}$$

Question 28

Use the square root property to solve the equation.

- $$x ^ { 2 } + 14 x + 58 = 0$$

A) $$- 7 + 3 i$$
B) $$- 7 \pm 9 \mathrm { i }$$
C) $$- 7 \pm 3 \mathrm { i }$$
D)-4, -10

Question 29

Solve the equation by the quadratic formula.

- $$x ^ { 2 } + 7 x - 18 = 0$$

A)-2, 9
B)-9, 2
C)-9, 1
D)9, 2

Question 30

Solve the equation by completing the square.

- $$49 c ^ { 2 } + 33 = 98 c$$

A) $$- \frac { 11 } { 7 } , - \frac { 3 } { 7 }$$
B) $$\frac { 11 } { 7 } , \frac { 3 } { 7 }$$
C) $$\frac { 11 } { 49 } , \frac { 3 } { 49 }$$
D) $$\frac { 3 } { 49 } , \frac { 30 } { 49 }$$

Question 31

Solve the equation by completing the square.

-x $$x ^ { 2 } + 14 x + 58 = 0$$

A) $$- 7 \pm 9 i$$
B)-10, -4
C) $$- 7 \pm 3 i$$
D)-7 + 3i

Question 32

Solve the equation by completing the square.

- $$3 z ^ { 2 } = \frac { 3 } { 2 } z + 2$$

A) $$\frac { - 3 \pm \sqrt { 105 } } { 12 }$$
B) $$\frac { 3 \pm \sqrt { 105 } } { 12 }$$
C) $$\frac { 3 \pm \sqrt { 105 } } { 6 }$$
D) $$\frac { - 3 \pm \sqrt { 57 } } { 6 }$$

Question 33

Solve the problem.
The length of a vegetable garden is 6 feet longer than its width. If the area of the garden is 112 square feet, find its dimensions.

A)w = 7 ft; l = 15 ft
B)w = 9 ft; l = 15 ft
C)w = 7 ft; l = 13 ft
D)w = 8 ft; l = 14 ft

Question 34

Use the square root property to solve the equation.

- $$x ^ { 2 } + x + 7 = 0$$

A) $$- \frac { 1 } { 2 } \pm \frac { \sqrt { 27 } } { 2 } \mathrm { i }$$
B) $$\frac { - 1 \pm \sqrt { 27 } } { 2 }$$
C) $$\frac { 1 \pm \sqrt { 27 } } { 2 }$$
D) $$\frac { 1 } { 2 } \pm \frac { \sqrt { 27 } } { 2 } \mathrm { i }$$

Question 35

Solve the problem.
The product of a number and 3 less than the number is 18. Find the number.

A)-6 or 3
B)-7 or 2
C)-3 or 6
D)-2 or 7

Question 36

Solve the problem.

-A ladder that is 13 feet long is 5 feet from the base of a wall. How far up the wall does the ladder reach?

A)144 ft
B) $$\sqrt { 194 } \mathrm { ~ft }$$
C) $$2 \sqrt { 2 } \mathrm { ~ft }$$
D)12 ft

Question 37

Solve the equation by completing the square.

- $$\frac { 4 } { 3 } p ^ { 2 } - \frac { 5 } { 3 } p + \frac { 7 } { 3 } = 0$$

A) $$\frac { 5 \pm \mathrm { i } \sqrt { 87 } } { 4 }$$
B) $$\frac { 5 \pm \sqrt { 87 } } { 8 }$$
C) $$\frac { 5 \pm i \sqrt { 87 } } { 8 }$$
D) $$\frac { - 5 \pm \sqrt { 87 } } { 8 }$$

Question 38

Solve the problem.

-If a $2000 investment compounded to $2205.00 after 2 years, compounded annually, find the annual interest rate of the investment. Use the formula, $$\mathrm { A } = \mathrm { p } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$$ to solve to solve.

A)0.5%
B)50%
C)5%
D)500%

Question 39

Solve the problem.

-A 30-foot pole is supported by two wires that extend from the top of the pole to points that are each 12 feet from the base of the pole. Find the total length of the two wires.

A) $$6 \sqrt { 29 } \mathrm { ~ft }$$
B)84 ft
C)2088 ft
D) $$12 \sqrt { 29 } \mathrm { ~ft }$$

Question 40

Solve the problem.

-Imelda inherited $20,000 and invested it in a mutual fund for two years. At the end of the two years, her investment had grown to $29,768. Find the annual interest rate that would yield this amount of money, if the
Interest is compounded annually. Use the formula,nnually. Use the formula, $$A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$$ to solve to solve.

A)0.22%
B)220%
C)22%
D)2.2%

Question 41

Solve the equation by the quadratic formula.

- $$( x + 5 ) ( x - 4 ) = 4$$

A) $$\frac { 1 \pm i \sqrt { 97 } } { 2 }$$
B) $$\frac { 1 \pm \sqrt { 97 } } { 2 }$$
C) $$\frac { - 1 \pm i \sqrt { 97 } } { 2 }$$
D) $$\frac { - 1 \pm \sqrt { 97 } } { 2 }$$

Question 42

Solve the equation by the quadratic formula.

- $$\frac { 2 } { 3 } c ^ { 2 } - \frac { 10 } { 3 } c + \frac { 4 } { 3 } = 0$$

A) $$\frac { - 10 \pm \sqrt { 17 } } { 4 }$$
B) $$\frac { - 5 \pm \sqrt { 17 } } { 2 }$$
C) $$\frac { 10 \pm \sqrt { 17 } } { 2 }$$
D) $$\frac { 5 \pm \sqrt { 17 } } { 2 }$$

Question 43

Solve the equation by the quadratic formula.

- $$x ^ { 2 } + 4 = 0$$

A)2
B) $$2 \mathrm { i }$$
C) $$\pm 2 \mathrm { i }$$
D) $$\pm 2$$

Question 44

Solve the equation by the quadratic formula.

- $$3 x ^ { 2 } + 12 x + 1 = 0$$

A) $$\frac { - 6 \pm \sqrt { 33 } } { 6 }$$
B) $$\frac { - 12 \pm \sqrt { 33 } } { 3 }$$
C) $$\frac { - 6 \pm \sqrt { 39 } } { 3 }$$
D) $$\frac { - 6 \pm \sqrt { 33 } } { 3 }$$

Question 45

Solve the equation by the quadratic formula.

- $$2 x ^ { 2 } + 12 x + 3 = 0$$

A) $$\frac { - 12 \pm \sqrt { 30 } } { 2 }$$
B) $$\frac { - 6 \pm \sqrt { 30 } } { 4 }$$
C) $$\frac { - 6 \pm \sqrt { 42 } } { 2 }$$
D) $$\frac { - 6 \pm \sqrt { 30 } } { 2 }$$

Question 46

Solve the equation by the quadratic formula.

- $$\frac { x ^ { 2 } } { 16 } + x + \frac { 21 } { 8 } = 0$$

A) $$8 \pm \sqrt { 42 }$$
B) $$- 16 + \sqrt { 42 }$$
C) $$- 8 \pm \sqrt { 22 }$$
D) $$8 + \sqrt { 22 }$$

Question 47

Solve the equation by the quadratic formula.

- $$x ^ { 2 } - 10 x + 50 = 0$$

A)5 + 5i
B)0, 10
C) $$5 \pm 5 i$$
D) $$5 \pm 25 \mathrm { i }$$

Question 48

Solve the equation by the quadratic formula.

- $$( x + 3 ) ( x - 1 ) = 4$$

A) $$1 \pm i \sqrt { 3 }$$
B) $$- 1 \pm i \sqrt { 3 }$$
C) $$- 1 \pm \sqrt { 11 }$$
D) $$1 \pm \sqrt { 11 }$$

Question 49

Solve the equation by the quadratic formula.

- $$3 x ^ { 2 } = 33$$

A)16.5
B)12
C) $$\pm 11$$
D) $$\pm \sqrt { 11 }$$

Question 50

Solve the equation by the quadratic formula.

- $$2 x ^ { 2 } + 12 x + 36 = 0$$

A)-3 + 3i
B)-6, 0
C) $$- 3 \pm 3 i$$
D) $$- 3 \pm 9 \mathrm { i }$$

Question 51

Solve the equation by the quadratic formula.

- $$4 x ^ { 2 } + 10 x = - 2$$

A) $$\frac { - 10 \pm \sqrt { 17 } } { 4 }$$
B) $$\frac { - 5 \pm \sqrt { 17 } } { 4 }$$
C) $$\frac { - 5 \pm \sqrt { 33 } } { 4 }$$
D) $$\frac { - 5 \pm \sqrt { 17 } } { 8 }$$

Question 52

Solve the equation by the quadratic formula.

- $$2 x ^ { 2 } = - 6 x - 2$$

A) $$\frac { - 3 \pm \sqrt { 5 } } { 4 }$$
B) $$\frac { - 3 \pm \sqrt { 5 } } { 2 }$$
C) $$\frac { - 3 \pm \sqrt { 13 } } { 2 }$$
D) $$\frac { - 6 \pm \sqrt { 5 } } { 2 }$$

Question 53

Solve the equation by the quadratic formula.

- $$x ^ { 2 } + x + 7 = 0$$

A) $$\frac { 1 } { 2 } \pm \frac { \sqrt { 27 } } { 2 } \mathrm { i }$$
B) $$\frac { - 1 \pm \sqrt { 27 } } { 2 }$$
C) $$- \frac { 1 } { 2 } \pm \frac { \sqrt { 27 } } { 2 } \mathrm { i }$$
D) $$\frac { 1 \pm \sqrt { 27 } } { 2 }$$

Question 54

Solve the equation by the quadratic formula.

- $$x ^ { 2 } + 7 x + 5 = 0$$

A) $$\frac { - 7 \pm \sqrt { 69 } } { 2 }$$
B) $$\frac { - 7 \pm \sqrt { 29 } } { 14 }$$
C) $$\frac { 7 \pm \sqrt { 29 } } { 2 }$$
D) $$\frac { - 7 \pm \sqrt { 29 } } { 2 }$$

Question 55

Solve the equation by the quadratic formula.

- $$3 n ^ { 2 } - 9 n = \frac { 1 } { 3 }$$

A) $$\frac { - 9 \pm \sqrt { 77 } } { 6 }$$
B) $$\frac { 9 \pm \sqrt { 77 } } { 6 }$$
C) $$\frac { 9 \pm \sqrt { 85 } } { 6 }$$
D) $$\frac { - 9 \pm \sqrt { 85 } } { 6 }$$

Question 56

Solve the equation by the quadratic formula.

- $$2 x ^ { 2 } - 14 = 0$$

A) $$\pm \sqrt { 14 }$$
B) $$\sqrt { 7 }$$
C) $$\pm \sqrt { 7 }$$
D) $$\pm \frac { \sqrt { 14 } } { 2 }$$

Question 57

Solve the equation by the quadratic formula.

- $$7 x ^ { 2 } - 55 x - 8 = 0$$

A) $$- \frac { 1 } { 7 } , 7$$
B) $$- \frac { 1 } { 7 } , 8$$
C)-7, 8
D) $$- \frac { 1 } { 7 } , \frac { 1 } { 55 }$$

Question 58

Solve the equation by the quadratic formula.

- $$3 x ^ { 2 } + x - 6 = 0$$

A) $$\frac { - 1 \pm \sqrt { 73 } } { 2 }$$
B) $$\frac { - 1 \pm \mathrm { i } \sqrt { 73 } } { 6 }$$
C) $$\frac { - 1 \pm \sqrt { 73 } } { 6 }$$
D) $$\frac { 1 \pm \sqrt { 73 } } { 6 }$$

Question 59

Solve the equation by the quadratic formula.

- $$16 x ^ { 2 } + 1 = 3 x$$

A) $$\frac { 3 \pm \mathrm { i } \sqrt { 55 } } { 32 }$$
B) $$\frac { - 3 \pm \sqrt { 55 } } { 32 }$$
C) $$\frac { 3 \pm \sqrt { 55 } } { 32 }$$
D) $$\frac { - 3 \pm \mathrm { i } \sqrt { 55 } } { 32 }$$

Question 60

Solve the equation by the quadratic formula.

- $$6 x ^ { 2 } = - 12 x - 3$$

A) $$\frac { - 12 \pm \sqrt { 2 } } { 2 }$$
B) $$\frac { - 2 \pm \sqrt { 2 } } { 12 }$$
C) $$\frac { - 2 \pm \sqrt { 2 } } { 2 }$$
D) $$\frac { - 2 \pm \sqrt { 6 } } { 2 }$$

Question 61

Write an equation that has the given solutions.

-1 $$1 + \sqrt { 7 } , 1 - \sqrt { 7 }$$

A) $$x ^ { 2 } + 2 x + 6 = 0$$
B) $$x ^ { 2 } + 6 = 0$$
C) $$x ^ { 2 } - 2 x - 6 = 0$$
D) $$x ^ { 2 } - 6 = 0$$

Question 62

Write an equation that has the given solutions.

- $$- \sqrt { 7 } , \sqrt { 7 }$$

A) $$x ^ { 2 } + 7 = 0$$
B) $$x ^ { 2 } - 7 = 0$$
C) $$x ^ { 2 } - 2 \sqrt { 7 } x + 7 = 0$$
D) $$x ^ { 2 } + 2 \sqrt { 7 } x - 7 = 0$$

Question 63

Write an equation that has the given solutions.

- $$\frac { 3 } { 4 } , \frac { 3 } { 8 }$$

A) $$x ^ { 2 } - \frac { 9 } { 8 } x + \frac { 9 } { 32 } = 0$$
B) $$x ^ { 2 } + \frac { 9 } { 8 } x + \frac { 9 } { 32 } = 0$$
C) $$x ^ { 2 } + \frac { 9 } { 32 } x + \frac { 9 } { 8 } = 0$$
D) $$x ^ { 2 } - \frac { 9 } { 32 } x + \frac { 9 } { 8 } = 0$$

Question 64

Write an equation that has the given solutions.

-7, 8

A) $$x ^ { 2 } + 56 x + 15 = 0$$
B) $$x ^ { 2 } - 15 x + 56 = 0$$
C) $$x ^ { 2 } - 56 x + 15 = 0$$
D) $$x ^ { 2 } + 15 x + 56 = 0$$

Question 65

Write an equation that has the given solutions.

- $$- 6 i , 6 i$$

A) $$x ^ { 2 } - 36 = 0$$
B) $$x ^ { 2 } + 36 = 0$$
C) $$x ^ { 2 } + 12 x + 36 = 0$$
D) $$x ^ { 2 } - 12 x - 36 = 0$$

Question 66

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.

- $$x ^ { 2 } + 7 x + 6 = 0$$

A)two real solutions
B)one real solution
C)no real solution

Question 67

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.

- $$x ^ { 2 } + 6 x + 9 = 0$$

A)one real solution
B)no real solution
C)two real solutions

Question 68

Write an equation that has the given solutions.

--4, -3

A) $$x ^ { 2 } - 12 x - 7 = 0$$
B) $$x ^ { 2 } + 7 x + 12 = 0$$
C) $$x ^ { 2 } - 7 x + 12 = 0$$
D) $$x ^ { 2 } + 12 x - 7 = 0$$

Question 69

Write an equation that has the given solutions.

- $$\frac { 3 } { 4 } , \frac { 3 } { 8 }$$

A) $$32 x ^ { 2 } + 9 x + 36 = 0$$
B) $$32 x ^ { 2 } - 36 x + 9 = 0$$
C) $$32 x ^ { 2 } + 36 x + 9 = 0$$
D) $$32 x ^ { 2 } - 9 x + 36 = 0$$

Question 70

Write an equation that has the given solutions.

- $$- 2 \sqrt { 10 } , 2 \sqrt { 10 }$$

A) $$x ^ { 2 } + 4 \sqrt { 10 } x - 40 = 0$$
B) $$x ^ { 2 } - 40 = 0$$
C) $$x ^ { 2 } + 40 = 0$$
D) $$x ^ { 2 } - 4 \sqrt { 10 } x + 40 = 0$$

Question 71

Write an equation that has the given solutions.

--6, 9

A) $$x ^ { 2 } + 54 x + 3 = 0$$
B) $$x ^ { 2 } - 3 x - 54 = 0$$
C) $$x ^ { 2 } - 54 x + 3 = 0$$
D) $$x ^ { 2 } + 3 x - 54 = 0$$

Question 72

Solve the problem.
The area of a rectangle is given. Find the length and width of the rectangle.

A)w = 4; l = 12
B)w = 5; l = 11
C)w = 4; l = 10
D)w = 6; l = 12

Question 73

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.

- $$1 - 4 x ^ { 2 } = - 6 x - 1$$

A)no real solution
B)one real solution
C)two real solutions

Question 74

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.

- $$3 + 6 x ^ { 2 } = - 3 x$$

A)two real solutions
B)one real solution
C)no real solution

Question 75

Determine all real values of the variable for which the function has the value indicated.

- $$g ( x ) = x ^ { 2 } + 4 x + 11 , g ( x ) = 23$$

A)-2, 6
B)-6, 2
C) $$\frac { 4 \pm \sqrt { 23 } } { 2 }$$
D)no real numbers

Question 76

Determine all real values of the variable for which the function has the value indicated.

- $$h ( a ) = 5 a ^ { 2 } + 12 a + 6$$

A) $$\frac { - 6 \pm \sqrt { 66 } } { 5 }$$
B) $$\frac { - 6 \pm \sqrt { 6 } } { 5 }$$
C) $$\frac { - 12 \pm \sqrt { 6 } } { 5 }$$
D)no real numbers

Question 77

Use the discriminant to determine whether the equation has two distinct real solutions, a single real solution, or no real
solution.

- $$7 x ^ { 2 } = 2 x - 5$$

A)one real solution
B)two real solutions
C)no real solution

Question 78

Determine all real values of the variable for which the function has the value indicated.

- $$p ( t ) = 7 t ^ { 2 } + 3 t + 49 , g ( t ) = 10$$

A) $$\frac { - 3 \pm \sqrt { 55 } } { 7 }$$
B) $$\frac { - 3 \pm \sqrt { 1381 } } { 14 }$$
C) $$\frac { 3 \pm \sqrt { 1381 } } { 14 }$$
D)no real numbers

Question 79

Solve the equation by the quadratic formula.

- $$x ^ { 2 } + 12 x + 21 = 0$$

A) $$6 \pm \sqrt { 21 }$$
B) $$6 + \sqrt { 15 }$$
C) $$- 12 + \sqrt { 21 }$$
D) $$- 6 \pm \sqrt { 15 }$$

Question 80

Write an equation that has the given solutions.

- $$7 + i , 7 - i$$

A) $$x ^ { 2 } + 14 x - 50 = 0$$
B) $$x ^ { 2 } + 14 x - 48 = 0$$
C) $$x ^ { 2 } - 14 x + 48 = 0$$
D) $$x ^ { 2 } - 14 x + 50 = 0$$