9 The polynomial \(f ( x )\) is given by
$$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + x - 4 .$$
- (a) Show that ( \(\mathrm { x } + 1\) ) is a factor of \(\mathrm { f } ( \mathrm { x } )\).
(b) Hence find the exact roots of the equation \(f ( x ) = 0\). - (a) Show that the equation
$$2 \log _ { 2 } ( x + 3 ) + \log _ { 2 } x - \log _ { 2 } ( 4 x + 2 ) = 1$$
can be written in the form \(f ( x ) = 0\).
(b) Explain why the equation
$$2 \log _ { 2 } ( x + 3 ) + \log _ { 2 } x - \log _ { 2 } ( 4 x + 2 ) = 1$$
has only one real root and state the exact value of this root.