1.
Let f(x)=a10axa1ax2axaf(x) = \begin{vmatrix} a & -1 & 0 \\ ax & a & -1 \\ ax^2 & ax & a \end{vmatrix}, aRa \in \mathbb{R}. Then the sum of the squares of all the values of aa for which 2f(10)+f(5)+100=02f'(10) + f'(5) + 100 = 0 is