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The equation $x^2-kx-12=0$ has only integer solutions for certain positive integers $k$. What is the sum of all such values of $k$?

 Feb 19, 2021

Best Answer 

 #1
avatar+31281 
+1

Factors of  -12    that when added = positive k    (note that k has a negative sign in front of it in the equation)

1   -12             added together = k  =   (-)   11

2     -6                                                  (-)     4

3    - 4                                                  (-)     1

example :   (x+1)(x-12) = x^2 -11x -12      k = 11

 

11 + 4 + 1 = 16

 Feb 19, 2021
 #1
avatar+31281 
+1
Best Answer

Factors of  -12    that when added = positive k    (note that k has a negative sign in front of it in the equation)

1   -12             added together = k  =   (-)   11

2     -6                                                  (-)     4

3    - 4                                                  (-)     1

example :   (x+1)(x-12) = x^2 -11x -12      k = 11

 

11 + 4 + 1 = 16

ElectricPavlov Feb 19, 2021

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