derivatives and determinant

Let f(x)=(x-x_1)(x-x_2)...(x-x_n)where the numbers x_1,x_2,...,x_n-pairwise distinct and a_{ii}=f''(x_i), a_{ij}=(f(x_i)-f(x_j))/(x_i-x_j).
What information we can say about such a matrix Can we say that detA=0 ?

I'd be grateful if someone could help me
Regards
eugene
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