5 Throughout this question the use of a calculator is not permitted.
It is given that the complex number \(- 1 + ( \sqrt { } 3 ) \mathrm { i }\) is a root of the equation
$$k x ^ { 3 } + 5 x ^ { 2 } + 10 x + 4 = 0$$
where \(k\) is a real constant.
- Write down another root of the equation.
- Find the value of \(k\) and the third root of the equation.