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The diagram shows the curve \(y = 2 x ^ { 5 } + 3 x ^ { 3 }\) and the line \(y = 2 x\) intersecting at points \(A , O\) and \(B\).
- Show that the \(x\)-coordinates of \(A\) and \(B\) satisfy the equation \(2 x ^ { 4 } + 3 x ^ { 2 } - 2 = 0\).
- Solve the equation \(2 x ^ { 4 } + 3 x ^ { 2 } - 2 = 0\) and hence find the coordinates of \(A\) and \(B\), giving your answers in an exact form.