9x^2-6x+1=0

Question

Find the value of the discriminant 

describe the number and types of roots

find the exact solutions bybusing the quadratic formula

 

Answer 1

Hi Jazlynn, The discriminant is b squared minus 4ac.

 

In this case it would be minus 6 squared minus 4 times 9 times 1 or 36-36 or zero.

 

Therefore the roots are real but there is only one repeated solution. (3x-1)(3x-1) x=1/3.

Answer 2

Jazlynn,

 

David did a great job explaining the answer to you.  Using the quadratic formula is not so tough.  It takes practice.   

 

x =  -b±√b² -4ac

             2a

      

a = 9

b = -6

c = 1

 

So,

 

x = -(-6)±√(-6)² - 4(9)(1)

                2(9)

 

x = 6±√36 - 36

            18

 

x = 6 ± 0

         18

 

x = 1/3 

 

Same answer, but this time using the quadratic equation.  :)

 

Bill

El Paso, TX