Intermediate Algebra (11th edition)

522 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

SUMMARY EXERCISES on Solving Quadratic Equations

We have introduced four methods for solving quadratic equations written in standard form

ax^2 +bx+c=0.

Concept Check Decide whether factoring,thesquare root property, or thequadratic for-

mula is most appropriate for solving each quadratic equation. Do not actually solve.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   

Solve each quadratic equation by the method of your choice.

7. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   


8. 
   
   
   
   11. 
       
       
       
       12. 
           
       
       
       
       
   
   
   
   


9. *14. 15.


10. 
    
    
    
    17. 
        
        
        
        18. 
            
        
        
        
        
    
    
    
    

19. 20. *21.

22. 23. 24.

25. 26. 27.

28. *29. 30.

31. 
    
    
    
    32. 213 x- 122 + 513 x- 12 =- 2
    
    
    
    

4

r^2

+ 3 =

1

r

z=

B

5 z+ 3

2

w^2 = 169 3 p^2 = 6 p- 4

r^2 - 72 = 0 - 3 x^2 + 4 x=- 4 x^2 - 5 x- 36 = 0

5 x^6 + 2 x^3 - 7 = 0 4 t^2 - 12 t+ 9 = 0 x 23 = 22 - x

t^4 + 14 = 9 t^28 x^2 - 4 x= 2 z^2 + z+ 1 = 0

2

x

+

1

x- 2

=

5

3

x^4 - 10 x^2 + 9 = 0 12 x+ 322 = 8

2 r^2 - 4 r+ 1 = 0 x^2 =- 12 x 22 = 25 x- 2

3 x^2 = 3 - 8 x

5

x

+

12

x^2

1 x- 322 = 25 = 2

p^2 = 7 6 x^2 - x- 15 = 0 n^2 + 6 n+ 4 = 0

2 x^2 + 3 x= 1 3 x^2 = 2 - 5 x x^2 = 5

12 x+ 322 = 4 4 x^2 - 3 x= 1 x^2 + 5 x- 8 = 0

*This exercise requires knowledge of complex numbers.

Solve each equation for the specified variable. See Section 2.2.

83. for W 84. for h 85.F= for C

9

5

a= C+ 32

1

2

P= 2 L+ 2 W bh

PREVIEW EXERCISES

Method Advantages Disadvantages

Factoring

Square root

property

Completing

the square

Quadratic

formula

This is usually the

fastest method.

This is the simplest

method for solving

equations of the form

This method can

always be used,

although most people

prefer the quadratic

formula.

This method can

always be used.

1 ax+b 22 =c.

Not all polynomials are

factorable. Some factorable

polynomials are difficult to factor.

Few equations are given in

this form.

It requires more steps than

other methods.

Sign errors are common

when evaluating 2 b^2 - 4 ac.

*