2021 YIJC P1 Q6

Do not use a calculator in answering this question.

1. One of the roots of the equation \(2{{z}^{3}}-9{{z}^{2}}+30z+b=0\) is \(1+a\mathrm{i}\), where \(a\) and \(b\) are non-zero real numbers. Find the values of \(a\) and \(b\) are non-zero real numbers. Find the values of \(a\) and \(b\) and the roots of this equation.[5]
2. Hence solve the equation \(b{{z}^{3}}+30{{z}^{2}}-9z+2=0\).[2]