- The cubic equation
$$x ^ { 3 } - 7 x ^ { 2 } - 12 x + 6 = 0$$
has roots \(\alpha , \beta\) and \(\gamma\).
Without solving the equation, determine a cubic equation whose roots are ( \(\alpha + 2\) ), \(( \beta + 2 )\) and \(( \gamma + 2 )\), giving your answer in the form \(w ^ { 3 } + p w ^ { 2 } + q w + r = 0\), where \(p , q\) and \(r\) are integers to be found.