if k is a positive integer less than 26, what is the total number of integral solution for the equation x2+10x-k=0

Question

 help me 

Answer 1

Eligible k values run from 1 to 25, any of which would have to be split into two factors that differ by ten.

 

obviously 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 won't work, nor will 25.

 

What about 12?  (x+12)(x-2) = 0  i.e. x² + 10x -24.

 

I leave it to you to determine if any other k values (13 to 22) will work.