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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.

 Jun 22, 2024
 #1
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Let's first combine all like terms. We have

\(x^2+kx-9x+16\\ x^2+(k-9)x+16\)

 

Since we need this to be a difference of squares, k-9 must be 2 times the square root of 16. 

Thus, we have

\(k-9=8\\ k=17\)

 

So k is 17.

 

So our answer is 17. 

 

Thanks! :) 

 Jun 22, 2024

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