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Algebra for College Students

Mark Dugopolski

Chapter 8

Quadratic Equations, Functions, and Inequalities - all with Video Answers

Educators


Section 1

Factoring and Completing the Square

01:02

Problem 1

What are the three methods discussed in this section for solving a quadratic equation?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:55

Problem 2

Which quadratic equations can be solved by the even-root property?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:10

Problem 3

How do you find the last term for a perfect square trinomial when completing the square?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:19

Problem 4

How do you complete the square when the leading coefficient is not 1?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:12

Problem 5

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$x^{2}-x-6=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:50

Problem 6

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$x^{2}+6 x+8=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:14

Problem 7

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$a^{2}+2 a=15$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:57

Problem 8

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$w^{2}-2 w=15$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:58

Problem 9

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$2 x^{2}-x-3=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:10

Problem 10

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$6 x^{2}-x-15=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:49

Problem 11

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$y^{2}+14 y+49=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:46

Problem 12

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$a^{2}-6 a+9=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:45

Problem 13

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$a^{2}-16=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 14

Solve by factoring.
See Example 1.
See the Strategy for Solving Quadratic Equations by Factoring box on page 522.
$$4 w^{2}-25=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:28

Problem 15

Use the even-root property to solve each equation.
$$x^{2}=81$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:24

Problem 16

Use the even-root property to solve each equation.
$$x^{2}=\frac{9}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:29

Problem 17

Use the even-root property to solve each equation.
$$x^{2}=\frac{16}{9}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:42

Problem 18

Use the even-root property to solve each equation.
$$a^{2}=32$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:37

Problem 19

Use the even-root property to solve each equation.
$$(x-3)^{2}=16$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:43

Problem 20

Use the even-root property to solve each equation.
$$(x+5)^{2}=4$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:37

Problem 21

Use the even-root property to solve each equation.
$$(z+1)^{2}=5$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:51

Problem 22

Use the even-root property to solve each equation.
$$(a-2)^{2}=8$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:08

Problem 23

Use the even-root property to solve each equation.
$$\left(w-\frac{3}{2}\right)^{2}=\frac{7}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:58

Problem 24

Use the even-root property to solve each equation.
$$\left(w+\frac{2}{3}\right)^{2}=\frac{5}{9}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:37

Problem 25

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$x^{2}+2 x$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:34

Problem 26

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$m^{2}+14 m$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:48

Problem 27

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$x^{2}-3 x$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:38

Problem 28

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$w^{2}-5 w$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:55

Problem 29

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$y^{2}+\frac{1}{4} y$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 30

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$z^{2}+\frac{3}{2} z$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:41

Problem 31

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$x^{2}+\frac{2}{3} x$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:53

Problem 32

Find the perfect square trinomial whose first two terms are given. See Example 3.
$$p^{2}+\frac{6}{5} p$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:30

Problem 33

Factor each perfect square trinomial. See Example 4.
$$x^{2}+8 x+16$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:32

Problem 34

Factor each perfect square trinomial. See Example 4.
$$x^{2}-10 x+25$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:42

Problem 35

Factor each perfect square trinomial. See Example 4.
$$y^{2}-5 y+\frac{25}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:37

Problem 36

Factor each perfect square trinomial. See Example 4.
$$w^{2}+w+\frac{1}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:38

Problem 37

Factor each perfect square trinomial. See Example 4.
$$z^{2}-\frac{4}{7} z+\frac{4}{49}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:40

Problem 38

Factor each perfect square trinomial. See Example 4.
$$m^{2}-\frac{6}{5} m+\frac{9}{25}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:48

Problem 39

Factor each perfect square trinomial. See Example 4.
$$t^{2}+\frac{3}{5} t+\frac{9}{100}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:40

Problem 40

Factor each perfect square trinomial. See Example 4.
$$h^{2}+\frac{3}{2} h+\frac{9}{16}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:11

Problem 41

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}-2 x-15=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:05

Problem 42

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}-6 x-7=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:15

Problem 43

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$2 x^{2}-4 x=70$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:06

Problem 44

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$3 x^{2}-6 x=24$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:46

Problem 45

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$w^{2}-w-20=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:34

Problem 46

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$y^{2}-3 y-10=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:56

Problem 47

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$q^{2}+5 q=14$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:27

Problem 48

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$z^{2}+z=2$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:06

Problem 49

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$2 h^{2}-h-3=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:05

Problem 50

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$2 m^{2}-m-15=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:56

Problem 51

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}+4 x=6$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:12

Problem 52

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}+6 x-8=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:37

Problem 53

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}+8 x-4=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:41

Problem 54

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}+10 x-3=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:37

Problem 55

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}+5 x+5=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:33

Problem 56

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$x^{2}-7 x+4=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:04

Problem 57

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$4 x^{2}-4 x-1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:02

Problem 58

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$4 x^{2}+4 x-2=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:05

Problem 59

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$2 x^{2}+3 x-4=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:01

Problem 60

Solve by completing the square.
See Examples 5–7.
See the Strategy for Solving Quadratic Equations by
Completing the Square box on page 526. Use your calculator to check.
$$2 x^{2}+5 x-1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
03:01

Problem 61

Solve each equation by an appropriate method.
$$\sqrt{2 x+1}=x-1$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:40

Problem 62

Solve each equation by an appropriate method.
$$\sqrt{2 x-4}=x-14$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:59

Problem 63

Solve each equation by an appropriate method.
$$w=\frac{\sqrt{w+1}}{2}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
05:12

Problem 64

Solve each equation by an appropriate method.
$$y-1=\frac{\sqrt{y+1}}{2}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:53

Problem 65

Solve each equation by an appropriate method.
$$\frac{t}{t-2}=\frac{2 t-3}{t}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:36

Problem 66

Solve each equation by an appropriate method.
$$\frac{z}{z+3}=\frac{3 z}{5 z-1}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:44

Problem 67

Solve each equation by an appropriate method.
$$\frac{2}{x^{2}}+\frac{4}{x}+1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:10

Problem 68

Solve each equation by an appropriate method.
$$\frac{1}{x^{2}}+\frac{3}{x}+1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:49

Problem 69

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}+2 x+5=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:34

Problem 70

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}+4 x+5=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:21

Problem 71

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}-6 x+11=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:20

Problem 72

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}-8 x+19=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:22

Problem 73

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}=-\frac{1}{2}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:33

Problem 74

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}=-\frac{1}{8}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:58

Problem 75

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$x^{2}+12=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:46

Problem 76

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$-3 x^{2}-21=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:07

Problem 77

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$5 z^{2}-4 z+1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:00

Problem 78

Use completing the square to find the imaginary solutions to each equation. See Example 10.
$$2 w^{2}-3 w+2=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:35

Problem 79

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$x^{2}=-121$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:51

Problem 80

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$w^{2}=-225$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:25

Problem 81

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$4 x^{2}+25=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 82

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$5 w^{2}-3=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 83

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$\left(p+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:46

Problem 84

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$\left(y-\frac{2}{3}\right)^{2}=\frac{4}{9}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:52

Problem 85

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$5 t^{2}+4 t-3=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:44

Problem 86

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$3 v^{2}+4 v-1=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:40

Problem 87

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$m^{2}+2 m-24=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:41

Problem 88

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$q^{2}+6 q-7=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:45

Problem 89

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$(x-2)^{2}=-9$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:04

Problem 90

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$(2 x-1)^{2}=-4$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:46

Problem 91

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$-x^{2}+x+6=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:43

Problem 92

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$-x^{2}+x+12=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:23

Problem 93

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$x^{2}-6 x+10=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:16

Problem 94

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$x^{2}-8 x+17=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
04:47

Problem 95

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$2 x-5=\sqrt{7 x+7}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:30

Problem 96

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$\sqrt{7 x+29}=x+3$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
04:07

Problem 97

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$\frac{1}{x}+\frac{1}{x-1}=\frac{1}{4}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:54

Problem 98

Find all real or imaginary solutions to each equation.
Use the method of your choice.
$$\frac{1}{x}-\frac{2}{1-x}=\frac{1}{2}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:09

Problem 99

Find the real solutions to each equation by examining the following graphs on the next page.
$$x^{2}+2 x-15=0$$
(Graph can't copy)

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:56

Problem 100

Find the real solutions to each equation by examining the following graphs on the next page.
$$100 x^{2}+20 x-3=0$$
(Graph can't copy)

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:50

Problem 101

Find the real solutions to each equation by examining the following graphs on the next page.
$$x^{2}+4 x+15=0$$
(Graph can't copy)

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:43

Problem 102

Find the real solutions to each equation by examining the following graphs on the next page.
$$100 x^{2}-60 x+9=0$$
(Graph can't copy)

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:15

Problem 103

Solve each problem.
The formula $1211.1 L=C A^{2} S$ is used to determine the approach speed for landing an aircraft, where $L$ is the gross weight of the aircraft in pounds, $C$ is the coefficient of lift, $S$ is the surface area of the wings in square feet ( $\mathrm{ft}^{2}$ ), and $A$ is approach speed in feet per second. Find $A$ for the Piper Cheyenne, which has a gross weight of 8700 lb, a coefficient of lift of $2.81,$ and wing surface area of $200 \mathrm{ft}^{2}$.

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:03

Problem 104

Solve each problem.
The period $T$ (time in seconds for one complete cycle) of a simple pendulum is related to the length $L$ (in feet) of the pendulum by the formula $8 T^{2}=\pi^{2} L .$ If a child is on a swing with a 10 -foot chain, then how long does it take to complete one cycle of the swing?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:56

Problem 105

Solve each problem.
Tropical Pools figures that its monthly revenue in dollars on the sale of $x$ above ground pools is given by $R=1500 x-3 x^{2},$ where $x$ is less than $25 .$ What number of pools sold would provide a revenue of $\$ 17,568 ?$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
05:30

Problem 106

Solve each problem.
In 1981 Vladimir Poliakov (USSR) set a world record of $19 \mathrm{ft} \frac{3}{4}$ in. for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The function $h=-16 t^{2}+36 t$ gives his height $t$ seconds after leaving the ground.
a) Use the formula to find the exact values of $t$ for which his height was 18 feet.
b) Use the accompanying graph to estimate the value of $t$ for which he was at his maximum height.
c) Approximately how long was he in the air?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:22

Problem 107

Which of the following equations is not a quadratic equation? Explain your answer.
a) $\pi x^{2}-\sqrt{5} x-1=0$
b) $3 x^{2}-1=0$
c) $4 x+5=0$
d) $0.009 x^{2}=0$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
04:47

Problem 108

Solve $x^{2}-4 x+k=0$ for $k=0,4,5,$ and 10.
a) When does the equation have only one solution?
b) For what values of $k$ are the solutions real?
c) For what values of $k$ are the solutions imaginary?

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:03

Problem 109

Write a quadratic equation of each of the following types, then trade your equations with those of a classmate. Solve the equations and verify that they are of the required types.
a) a single rational solution
b) two rational solutions
c) two irrational solutions
d) two imaginary solutions

Cullen Miller
Cullen Miller
Numerade Educator
01:35

Problem 110

In Section 8.2 we will solve $a x^{2}+b x+c=0$ for $x$ by completing the square. Try it now without looking ahead.

Nez Nikoo
Nez Nikoo
Numerade Educator
00:44

Problem 111

For each equation, find approximate solutions rounded to two decimal places.
$$x^{2}-7.3 x+12.5=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:12

Problem 112

For each equation, find approximate solutions rounded to two decimal places.
$$1.2 x^{2}-\pi x+\sqrt{2}=0$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:47

Problem 113

For each equation, find approximate solutions rounded to two decimal places.
$$2 x-3=\sqrt{20-x}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:09

Problem 114

For each equation, find approximate solutions rounded to two decimal places.
$$x^{2}-1.3 x=22.3-x^{2}$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator