Question 865063
Maybe putting attention on the discriminant is more efficient.
{{{D=(-k)^2-4*k=k^2-4k}}}.


You want no real solutions, so this means {{{D<0}}}.
{{{highlight_green(k^2-4k<0)}}}, and you want to know the solutions to this for k.
{{{k(k-4)<0}}}
Critical points are 0 and 4.  If you cannot accept this logically, then you need help specifically for this.


Assuming you know how to accept those critical points for k,  you can test intervals which those critical points make on the k number line.
-
Interval {{{k<0}}}, example point k=-1.
k(k-4)=(-)(-)=(+)>0
This interval does not work.
-
Interval {{{0<k<4}}}, example point k=1.
k(k-4)=(+)(-)=(-)<0
THIS interval WORKS.
-
Interval {{{4<k}}}, example point k=5.
k(k-4)=(+)(+)>0
This interval does not work.


SOLUTION:  {{{highlight(highlight(0<k<4))}}}.