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George has a quadratic of the form x^2 + bx + 1/3, where b is a specific negative number. Using his knowledge of how to complete the square, George is able to rewrite this quadratic in the form (x + m)^2 + 1/10. What is b?

 Oct 12, 2020
 #1
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m will be  1/2 of b    

   2m = b

 

When completing the square yo wil have to subtract m^2  from the equation to keep it balanced

 

1/3 - m^2 = 1/10

- m^2 = 3/30 - 10/30

m^2 =  7/30

      

m = - sqrt 7/30     (we are told b is negative)

                            check   :          (x - sqrt (7/30) )^2    -   7/30   + 1/3                       -7/30  + 10/30  = 1/10

                                                   x^2 - 2 sqrt(7/30) x + 7/30    - 7/30 + 1/3 

                                                    x^2 - 2sqrt(7/30)x    + 1/3  

 

So b = 2m =  - 2 sqrt (7/30) 

 Oct 12, 2020

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