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: