2 The cubic equation $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1 = 0$ has roots $\alpha , \beta , \gamma$.\\
(a) Find the value of $\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }$.\\

(b) Use standard results from the list of formulae (MF19) to show that

$$\sum _ { r = 1 } ^ { n } \left( ( \alpha + r ) ^ { 2 } + ( \beta + r ) ^ { 2 } + ( \gamma + r ) ^ { 2 } \right) = n \left( n ^ { 2 } + a n + b \right)$$

where $a$ and $b$ are constants to be determined.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2023 Q2}}