Question

what is the smallest value of k that would make the roots of the equation x^2-2x-k imaginary? please help, no idea how to do this.

Answer 1

for imaginary roots, the discriminant < 0
b^2 - 4ac < 0
4 - 4(1)(-k) < 0
4 + 4k < 0
4k < -4
k < -1

Of course we cannot pin-point the smallest number below -1
If you claim that you have the "smallest number" , I will simply subtract 1 from it, and I would have a smaller number than yours, etc.