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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
 #1
avatar+129197 
+1

Simplify as

 

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

 

Note that

(x + 4) (x + 4) =  x^2 + 8x + 16  = (x + 4)^2

So

k -9  = 8

k =17

 

Also 

(x - 4) (x -4)  = x^2 - 8x + 16  = (x - 4)^2

So

k- 9 = -8

k = 1

 

17 +  1    =   18

 

 

cool cool cool

 Jan 14, 2024

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