8 A curve has equation \(y = 2 x ^ { 2 } - x - 1\) and a line has equation \(y = k ( 2 x - 3 )\), where \(k\) is a constant.
- Show that the \(x\)-coordinate of any point of intersection of the curve and the line satisfies the equation
$$2 x ^ { 2 } - ( 2 k + 1 ) x + 3 k - 1 = 0$$
- The curve and the line intersect at two distinct points.
- Show that \(4 k ^ { 2 } - 20 k + 9 > 0\).
- Find the possible values of \(k\).