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

eramsby1O1O Jun 22, 2024

#1**+1 **

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! :)

NotThatSmart Jun 22, 2024