2 The cubic equation $6 \mathrm { x } ^ { 3 } + \mathrm { px } ^ { 2 } - 3 \mathrm { x } - 5 = 0$, where $p$ is a constant, has roots $\alpha , \beta , \gamma$.\\
(a) Find a cubic equation whose roots are $\alpha ^ { 2 } , \beta ^ { 2 } , \gamma ^ { 2 }$.\\

(b) It is given that $\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 2 ( \alpha + \beta + \gamma )$.\\
(i) Find the value of $p$.\\

(ii) Find the value of $\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 }$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2020 Q2}}