9 The cubic polynomial \(x ^ { 3 } + a x ^ { 2 } + b x - 6\) is denoted by \(\mathrm { f } ( x )\).
- The remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ) is equal to the remainder when \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\). Show that \(b = - 4\).
- Given also that ( \(x - 1\) ) is a factor of \(\mathrm { f } ( x )\), find the value of \(a\).
- With these values of \(a\) and \(b\), express \(\mathrm { f } ( x )\) as a product of a linear factor and a quadratic factor.
- Hence determine the number of real roots of the equation \(\mathrm { f } ( x ) = 0\), explaining your reasoning.