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9x^2-6x+1=0

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2 Answers

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.

Comments

Thank you sooo much!! I have understood every concept that my teacher has given the class, but the quadratic formula had given me some difficulty.
 
No problem Jazlynn.  You are welcome!
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

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