Vieta's take too long

Algebra Level 5

100(a12+1)(a22+1)(a102+1)100 (a_1^2 + 1)(a_2^2 + 1)\cdots (a_{10}^2 + 1)

Let a1,a2,,a10a_1, a_2, \ldots,a_{10} denote the roots to the equation m=110mxm=0 \displaystyle \sum_{m=1}^{10} m x^m = 0 . Find the value of the expression above.

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