+0  
 
-1
4
1
avatar+1791 

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

 Mar 7, 2024
 #1
avatar+128794 
+1

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

 

We need to have the discriminant =   0 

 

(k - 9)^2  - 4 * 16  = 0

 

(k -9)^2  - 64 =  0

 

(k -9)^2   = 64      take both roots

 

k - 9  =  8                    k -9  = -8

 

k  =17                        k = 1

 

Sum of k's   =  17 + 1  =  18

 

 

cool cool cool

 Mar 7, 2024

2 Online Users

avatar