Solve, by factorising, the equation \(2 x ^ { 2 } - x - 3 = 0\).
Sketch the graph of \(y = 2 x ^ { 2 } - x - 3\).
Show that the equation \(x ^ { 2 } - 5 x + 10 = 0\) has no real roots.
Find the \(x\)-coordinates of the points of intersection of the graphs of \(y = 2 x ^ { 2 } - x - 3\) and \(y = x ^ { 2 } - 5 x + 10\). Give your answer in the form \(a \pm \sqrt { b }\).