7 The polynomial \(3 x ^ { 3 } + 2 x ^ { 2 } + a x + b\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( x - 1 )\) is a factor of \(\mathrm { p } ( x )\), and that when \(\mathrm { p } ( x )\) is divided by \(( x - 2 )\) the remainder is 10 .

1. Find the values of \(a\) and \(b\).
2. When \(a\) and \(b\) have these values, solve the equation \(\mathrm { p } ( x ) = 0\).