JEE Math Practice Question

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 $$\left[ {\begin{matrix} {{\alpha ^2}} & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c \\ \end{matrix} } \right]$$ 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

1. A.3
2. B.6
3. C.12
4. D.9