- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
$$f ( x ) = 4 x ^ { 3 } + 5 x ^ { 2 } - 10 x + 4 a \quad x \in \mathbb { R }$$
where \(a\) is a positive constant.
Given ( \(x - a\) ) is a factor of \(\mathrm { f } ( x )\),
- show that
$$a \left( 4 a ^ { 2 } + 5 a - 6 \right) = 0$$
- Hence
- find the value of \(a\)
- use algebra to find the exact solutions of the equation
$$f ( x ) = 3$$