8 (a) The quadratic equation $x ^ { 2 } - 2 x + 4 = 0$ has roots $\alpha$ and $\beta$.\\
(i) Write down the values of $\alpha + \beta$ and $\alpha \beta$.\\
(ii) Show that $\alpha ^ { 2 } + \beta ^ { 2 } = - 4$.\\
(iii) Hence find a quadratic equation which has roots $\alpha ^ { 2 }$ and $\beta ^ { 2 }$.\\
(b) The cubic equation $x ^ { 3 } - 12 x ^ { 2 } + a x - 48 = 0$ has roots $p , 2 p$ and $3 p$.\\
(i) Find the value of $p$.\\
(ii) Hence find the value of $a$.

\hfill \mbox{\textit{OCR FP1  Q8}}