To find when the curve and the line do not meet, we set the equations equal to each other:

\(kx^2 - 3x = x - k\)

Rearrange to form a quadratic equation:

\(kx^2 - 4x + k = 0\)

For the curve and line not to meet, the discriminant of the quadratic must be less than zero:

\(b^2 - 4ac < 0\)

Here, \(a = k\), \(b = -4\), and \(c = k\). Calculate the discriminant:

\((-4)^2 - 4(k)(k) < 0\)

\(16 - 4k^2 < 0\)

Rearrange:

\(4k^2 > 16\)

\(k^2 > 4\)

Taking the square root of both sides gives:

\(k > 2 \text{ or } k < -2\)