Matrices and Determinants

Let $\alpha$ be a root of the equation $(a - c){x^2} + (b - a)x + (c - b) = 0$ where a, b, c are distinct real numbers such that the matrix \left[ {\matrix{ {{\alpha ^2}} & \alpha & 1 \cr 1 & 1 & 1 \cr a & b & c \cr } } \right] is singular. Then, the value of ${{{{(a - c)}^2}} \over {(b - a)(c - b)}} + {{{{(b - a)}^2}} \over {(a - c)(c - b)}} + {{{{(c - b)}^2}} \over {(a - c)(b - a)}}$ is