4. The equation
$$x ^ { 4 } + A x ^ { 3 } + B x ^ { 2 } + C x + 225 = 0$$
where \(A , B\) and \(C\) are real constants, has
- a complex root \(4 + 3 \mathrm { i }\)
- a repeated positive real root
- Write down the other complex root of this equation.
- Hence determine a quadratic factor of \(x ^ { 4 } + A x ^ { 3 } + B x ^ { 2 } + C x + 225\)
- Deduce the real root of the equation.
- Hence determine the value of each of the constants \(A , B\) and \(C\)