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 ,+∞
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