Beginning Algebra, 11th Edition

Solving a Quadratic Equation with Fractions

Solve

Clear fractions. Multiply by the LCD, 10.

Distributive property

Multiply.

Subtract 4tand 2 to write in standard form.

Identify and.

Substitute into the

quadratic formula.

Simplify.

Add.

Factor.

Divide to write in

lowest terms.

t= 2  26

t=

(^2) A 2  (^26) B
2
t = 224 = 24 # 6 = 226

4  226

2

t=

4  224

2

t=

4  216 + 8

2

t=

- 1 - 42  21 - 422 - 41121 - 22

2112

a=1,b=-4, c=- 2

t^2 - 4 t- 2 = 0

t^2 = 4 t+ 2

t^2 = 10 a

2

5

tb + 10 a

1

5

b

10 a

1

10

t^2 b = 10 a

2

5

t+

1

5

b

1

10

t^2 =

2

5

t+

1

5

.

EXAMPLE 5

SECTION 9.3 Solving Quadratic Equations by the Quadratic Formula 571

NOTE The single solution of the equation in Example 4is a rational number. If all

solutions of a quadratic equation are rational, the equation can be solved by factoring.

OBJECTIVE 4 Solve quadratic equations with fractions.

NOW TRY
EXERCISE 5
Solve 121 x^2 =^12 x-^13.

NOW TRY ANSWER

5. 
   

   E 3  (^25) F
   Be careful
   here.
   The solution set is E 2  (^26) F. NOW TRY
   Complete solution available
   on the Video Resources on DVD
   9.3 EXERCISES
   If necessary, write each equation in standard form. Then identify the val-
   ues of a, b, and c. Do not actually solve the equation. See Example 1.

   
   


6. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


7. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   


8. 
   
   
   
   8. 
      
   
   
   
   


9. 
   
   
   
   10. 
       
   
   
   
   


10. 
    

    91 x- 121 x+ 22 = 8 12. 213 x- 1212 x+ 52 = 5

    
    

1 x- 321 x+ 42 = 0 1 x+ 721 x- 22 = 0

3 x^2 =- 7 x 9 x^2 = 8 x

• 2 x^2 + 3 x- 8 = 0 3 x^2 = 4 x+ 2 5 x^2 = 3 x- 6

3 x^2 + 4 x- 8 = 0 9 x^2 + 2 x- 3 = 0 - 8 x^2 - 2 x- 3 = 0

ax^2 +bx+c= 0