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 
is singular. Then, the value of \( \dfrac{(a-c)^2}{(b-a)(c-b)} + \dfrac{(b-a)^2}{(a-c)(c-b)} + \dfrac{(c-b)^2}{(a-c)(b-a)} \) is:
