5 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = 2 x ^ { 3 } + a x ^ { 2 } - 3 x - 4$$
where \(a\) is a constant. It is given that ( \(x - 4\) ) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(a\) and hence factorise \(\mathrm { p } ( x )\).
- Show that the equation \(\mathrm { p } \left( \mathrm { e } ^ { 3 y } \right) = 0\) has only one real root and find its exact value.