Ok, so x^2 - x + k = 0
Therefore:
delta = 1^2 - 4k
= 1 - 4k
Now, for one root, delta = 0
For no roots, delta < 0
If k >= 1/4, delta <= 0 (a.k.a. 1 or 0 roots)
Note if k < 0, one root will be always be negative
So if you want to count 0 as not positive, then 0 < k < 1/4