2. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
$$f ( x ) = a x ^ { 3 } + ( 6 a + 8 ) x ^ { 2 } - a ^ { 2 } x$$
where \(a\) is a positive constant.
Given \(\mathrm { f } ( - 1 ) = 32\)
- show that the only possible value for \(a\) is 3
- Using \(a = 3\) solve the equation
$$\mathrm { f } ( x ) = 0$$
- Hence find all real solutions of
- \(3 y + 26 y ^ { \frac { 2 } { 3 } } - 9 y ^ { \frac { 1 } { 3 } } = 0\)
- \(3 \left( 9 ^ { 3 z } \right) + 26 \left( 9 ^ { 2 z } \right) - 9 \left( 9 ^ { z } \right) = 0\)