+1911 Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
+37147 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!
