Find the set values of k for which the curve y=kx^2 -3x and the line y=x-k do not meet.
show your work ! : )

Hello : 
the system is : 
y=kx² -3x 
y=x-k
kx² -3x= x-k
kx² -4x+k =0(1)
the curve y=kx^2 -3x And the line y=x-k do not meet if (1) has not solutions
 k ≠ 0   (if : k=0    (1) : -4x=0  so  x=0)
the discriminant : Δ = b²-4ac     a = k     b= -4    c= k
Δ = (-4)²-4(k)(k) = 16-4k² =4(4-k²)
(1) has not solutions : Δ<0  
4(4-k²) <0  : 4-k² <0
 k² >4
  √ k² > √4    .
|k |>2
k>2 or k<-2
the set values is   :  S = ] -∞, -2[ ∪] 2 ,+∞ [