Matrices And Determinants

Let \(f(x) = \left| {\matrix{ a & { - 1} & 0 \cr {ax} & a & { - 1} \cr {a{x^2}} & {ax} & a \cr } } \right|,\,a \in R\). Then the sum of the squares of all the values of a, for which \(2f'(10) - f'(5) + 100 = 0\), is