Let $\alpha$ be a root of the equation $( a - c ) x ^ { 2 } + ( b - a ) x + ( c - b ) = 0$ where $a , \quad b , \quad c$ are distinct real numbers such that the matrix $\begin{pmatrix} \alpha ^ { 2 } & \alpha & 1 \end{pmatrix}$ is singular. Then the value of $\frac { ( a - c ) ^ { 2 } } { ( b - a )( c - b ) } + \frac { ( b - a ) ^ { 2 } } { ( a - c )( c - b ) } + \frac { ( c - b ) ^ { 2 } } { ( a - c )( b - a ) }$ is\\
(1) 6\\
(2) 3\\
(3) 9\\
(4) 12