Conjugate roots in an arithmetic sequence

The cubic equation \(x^3-12x^2+ax+b=0\), where \(a\) and \(b\) are real, has three roots in an arithmetic sequence. One root is \(4+3\mathrm{i}\).

1. State a second root and justify your answer.[2]
2. Show that the remaining root is \(4\).[2]
3. Determine \(a\) and \(b\).[4]