Let α be a root of the equation (a – c) x² + (b – a) x + (c – b) = 0 where a, b, c are distinct real numbers such that the matrix
[∝², ∝, 1]
[1, 1, 1]
[a, b, c] is singular. Then the value of (a-c)² /(b-a)(c-b) + (b-a)² / (a-c)(c-b) + (c-b)²/(a-c)(b-a) is
1)6
2)3
3)9
4)12