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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra</link> by Denny Burzynski and Wade Ellis, Jr. Methods of solving quadratic equations as well as the logic underlying each method are discussed. Factoring, extraction of roots, completing the square, and the quadratic formula are carefully developed. The zero-factor property of real numbers is reintroduced. The chapter also includes graphs of quadratic equations based on the standard parabola, y = x^2, and applied problems from the areas of manufacturing, population, physics, geometry, mathematics (numbers and volumes), and astronomy, which are solved using the five-step method. This module contains an exercise supplement for the chapter "Quadratic Equations".

Exercise Supplement

Solving Quadratic Equations ((Reference)) - Solving Quadratic Equations by Factoring ((Reference))

For the following problems, solve the equations.

Exercise 1

( x2 )( x5 )=0 ( x2 )( x5 )=0

Exercise 2

( b+1 )( b6 )=0 ( b+1 )( b6 )=0

Exercise 3

( a+10 )( a5 )=0 ( a+10 )( a5 )=0

Exercise 4

( y3 )( y4 )=0 ( y3 )( y4 )=0

Exercise 5

( m8 )( m+1 )=0 ( m8 )( m+1 )=0

Exercise 6

( 4y+1 )( 2y+3 )=0 ( 4y+1 )( 2y+3 )=0

Exercise 7

( x+2 )( 3x1 )=0 ( x+2 )( 3x1 )=0

Exercise 8

( 5a2 )( 3a10 )=0 ( 5a2 )( 3a10 )=0

Exercise 9

x( 2x+3 )=0 x( 2x+3 )=0

Exercise 10

( a5 ) 2 =0 ( a5 ) 2 =0

Exercise 11

( y+3 ) 2 =0 ( y+3 ) 2 =0

Exercise 12

c 2 =36 c 2 =36

Exercise 13

16 y 2 49=0 16 y 2 49=0

Exercise 14

6 r 2 36=0 6 r 2 36=0

Exercise 15

a 2 +6a+8=0 a 2 +6a+8=0

Exercise 16

r 2 +7r+10=0 r 2 +7r+10=0

Exercise 17

s 2 9s+8=0 s 2 9s+8=0

Exercise 18

y 2 =10y9 y 2 =10y9

Exercise 19

11y2=6 y 2 11y2=6 y 2

Exercise 20

16 x 2 3=2x 16 x 2 3=2x

Exercise 21

m 2 =4m4 m 2 =4m4

Exercise 22

3( y 2 8 )=7y 3( y 2 8 )=7y

Exercise 23

a( 4b+7 )=0 a( 4b+7 )=0

Exercise 24

x 2 64=0 x 2 64=0

Exercise 25

m 2 81=0 m 2 81=0

Exercise 26

9 x 2 25=0 9 x 2 25=0

Exercise 27

5 a 2 125=0 5 a 2 125=0

Exercise 28

8 r 3 6r=0 8 r 3 6r=0

Exercise 29

m 2 6m+5=0 m 2 6m+5=0

Exercise 30

x 2 +2x24=0 x 2 +2x24=0

Exercise 31

x 2 +3x=28 x 2 +3x=28

Exercise 32

20 a 2 3=7a 20 a 2 3=7a

Exercise 33

2 y 2 6y=8 2 y 2 6y=8

Exercise 34

a 2 +2a=1 a 2 +2a=1

Exercise 35

2 r 2 =53r 2 r 2 =53r

Solving Quadratic Equations Using the Method of Extraction of Roots ((Reference))

For the following problems, solve the equations using extraction of roots.

Exercise 36

y 2 =81 y 2 =81

Exercise 37

a 2 =121 a 2 =121

Exercise 38

x 2 =35 x 2 =35

Exercise 39

m 2 =2 m 2 =2

Exercise 40

r 2 =1 r 2 =1

Exercise 41

s 2 10=0 s 2 10=0

Exercise 42

4 x 2 64=0 4 x 2 64=0

Exercise 43

3 y 2 =75 3 y 2 =75

Exercise 44

Solve y 2 =4 a 2 y 2 =4 a 2 for y. y.

Exercise 45

Solve m 2 =16 n 2 p 4 m 2 =16 n 2 p 4 for m. m.

Exercise 46

Solve x 2 =25 y 4 z 10 w 8 x 2 =25 y 4 z 10 w 8 for x. x.

Exercise 47

Solve x 2 y 2 =0 x 2 y 2 =0 for y. y.

Exercise 48

Solve a 4 b 8 x 6 y 12 z 2 =0 a 4 b 8 x 6 y 12 z 2 =0 for a 2 . a 2 .

Exercise 49

( x2 ) 2 =9 ( x2 ) 2 =9

Exercise 50

( y+3 ) 2 =25 ( y+3 ) 2 =25

Exercise 51

( a+10 ) 2 =1 ( a+10 ) 2 =1

Exercise 52

( m+12 ) 2 =6 ( m+12 ) 2 =6

Exercise 53

( r8 ) 2 =10 ( r8 ) 2 =10

Exercise 54

( x1 ) 2 =5 ( x1 ) 2 =5

Exercise 55

( a2 ) 2 =2 ( a2 ) 2 =2

Exercise 56

Solve ( x2b ) 2 = b 2 ( x2b ) 2 = b 2 for x x

Exercise 57

Solve ( y+6 ) 2 =a ( y+6 ) 2 =a for y. y.

Exercise 58

Solve ( 2a5 ) 2 =c ( 2a5 ) 2 =c for a. a.

Exercise 59

Solve ( 3m11 ) 2 =2 a 2 ( 3m11 ) 2 =2 a 2 for m. m.

Solving Quadratic Equations Using the Method of Completing the Square ((Reference)) - Solving Quadratic Equations Using the Quadratic Formula ((Reference))

For the following problems, solve the equations by completing the square or by using the quadratic formula.

Exercise 60

y 2 8y12=0 y 2 8y12=0

Exercise 61

s 2 +2s24=0 s 2 +2s24=0

Exercise 62

a 2 +3a9=0 a 2 +3a9=0

Exercise 63

b 2 +b8=0 b 2 +b8=0

Exercise 64

3 x 2 2x1=0 3 x 2 2x1=0

Exercise 65

5 a 2 +2a6=0 5 a 2 +2a6=0

Exercise 66

a 2 =a+4 a 2 =a+4

Exercise 67

y 2 =2y+1 y 2 =2y+1

Exercise 68

m 2 6=0 m 2 6=0

Exercise 69

r 2 +2r=9 r 2 +2r=9

Exercise 70

3 p 2 +2p=7 3 p 2 +2p=7

Exercise 71

10 x 3 +2 x 2 22x=0 10 x 3 +2 x 2 22x=0

Exercise 72

6 r 3 +6 r 2 3r=0 6 r 3 +6 r 2 3r=0

Exercise 73

15 x 2 +2 x 3 =12 x 4 15 x 2 +2 x 3 =12 x 4

Exercise 74

6 x 3 6x=6 x 2 6 x 3 6x=6 x 2

Exercise 75

( x+3 )( x4 )=3 ( x+3 )( x4 )=3

Exercise 76

( y1 )( y2 )=6 ( y1 )( y2 )=6

Exercise 77

( a+3 )( a+4 )=10 ( a+3 )( a+4 )=10

Exercise 78

( 2m+1 )( 3m1 )=2 ( 2m+1 )( 3m1 )=2

Exercise 79

( 5r+6 )( r1 )=2 ( 5r+6 )( r1 )=2

Exercise 80

4 x 2 +2x3=3 x 2 +x+1 4 x 2 +2x3=3 x 2 +x+1

Exercise 81

5 a 2 +5a+4=3 a 2 +2a+5 5 a 2 +5a+4=3 a 2 +2a+5

Exercise 82

( m+3 ) 2 =11 ( m+3 ) 2 =11

Exercise 83

( r8 ) 2 =70 ( r8 ) 2 =70

Exercise 84

( 2x+7 ) 2 =51 ( 2x+7 ) 2 =51

Applications ((Reference))

For the following problems, find the solution.

Exercise 85

The revenue R, R, in dollars, collected by a certain manufacturer of inner tubes is related to the number x x of inner tubes sold by R=140016x+3 x 2 . R=140016x+3 x 2 . How many inner tubes must be sold to produce a profit of $1361?

Exercise 86

A study of the air quality in a particular city by an environmental group suggests that t t years from now the level of carbon monoxide, in parts per million, in the air will be A=0.8 t 2 +0.5t+3.3. A=0.8 t 2 +0.5t+3.3.
(a) What is the level, in parts per million, of carbon monoxide in the air now?
(b) How many years from now will the carbon monoxide level be at 6 parts per million?

Exercise 87

A contractor is to pour a concrete walkway around a community garden that is 15 feet wide and 50 feet long. The area of the walkway and garden is to be 924 square feet and of uniform width. How wide should the contractor make it?

Exercise 88

A ball thrown vertically into the air has the equation of motion h=144+48t16 t 2 h=144+48t16 t 2
(a) How high is the ball at t=0? t=0?
(b) How high is the ball at t=1? t=1?
(c) When does the ball hit the ground?

Exercise 89

The length of a rectangle is 5 feet longer than three times its width. Find the dimensions if the area is to be 138 square feet.

Exercise 90

The area of a triangle is 28 square centimeters. The base is 3 cm longer than the height. Find both the length of the base and the height.

Exercise 91

The product of two consecutive integers is 210. Find them.

Exercise 92

The product of two consecutive negative integers is 272. Find them.

Exercise 93

A box with no top and a square base is to be made by cutting out 3-inch squares from each corner and folding up the sides of a piece of cardboard. The volume of the box is to be 25 cubic inches. What size should the piece of cardboard be?

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