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Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

 Jan 14, 2024
 #2
avatar+36916 
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AI approval is a bit 'sucky' at present, so I have no idea what was posted for an answer....here is my answer:

 

In quadratic form 

x^2 + (k-9) x + 16        <====== determinant of this quadratic must = 0 for only one root

 

b^2 - 4 ac = 0 

(k-9)^2 -4(1)(16) = 0 

   k^2 - 18k + 17 = 0 

     ( k -1)(k-17)   = 0               shows k = 1 or 17     sum = 18 

 

 

(x -4)^2  = x^2 - 8x + 16       

(x+4)^2  = x^2 +8x + 16        ✔            Check!

 Jan 14, 2024

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