If the function $f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + 12 \mathrm { a } ^ { 2 } x + 1 , \mathrm { a } > 0$ has a local maximum at $x = \alpha$ and a local minimum at $x = \alpha ^ { 2 }$, then $\alpha$ and $\alpha ^ { 2 }$ are the roots of the equation :
(1) $x ^ { 2 } - 6 x + 8 = 0$
(2) $x ^ { 2 } + 6 x + 8 = 0$
(3) $8 x ^ { 2 } + 6 x - 1 = 0$
(4) $8 x ^ { 2 } - 6 x + 1 = 0$