Question

Can someone show me how to even do this problem.

Find all positive values for K for which each of the following can be factored.

x^2 + x - k

News flash: It can be factored with any term (although the roots may not be real roots).

Now if you mean factored with real values for the factors a and b, ...
IT has to add to one, multiply to k.

a+b=1
ab=k
k=0 is a solution, but zero is not positive nor negative.
k=2 a=2, b=-1
k=6 (a=+3, b=-2) is a solution
k=20 a=5, b=-4 is a solution
Now, finding all positive values for k will be a great task, because this goes on ad infinitum. Example...
k=8.4525 a= 3.45 b=-2.45


you got me here i don't understand. So how do i determine what to substitue/.