7 The quadratic equation
$$( 2 k - 3 ) x ^ { 2 } + 2 x + ( k - 1 ) = 0$$
where \(k\) is a constant, has real roots.
- Show that \(2 k ^ { 2 } - 5 k + 2 \leqslant 0\).
- Factorise \(2 k ^ { 2 } - 5 k + 2\).
- Hence, or otherwise, solve the quadratic inequality
$$2 k ^ { 2 } - 5 k + 2 \leqslant 0$$