8 A curve has equation \(y = x ^ { 2 } + ( 3 k - 4 ) x + 13\) and a line has equation \(y = 2 x + k\), where \(k\) is a constant.
- Show that the \(x\)-coordinate of any point of intersection of the line and curve satisfies the equation
$$x ^ { 2 } + 3 ( k - 2 ) x + 13 - k = 0$$
- Given that the line and the curve do not intersect:
- show that \(9 k ^ { 2 } - 32 k - 16 < 0\);
- find the possible values of \(k\).
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