Is Vieta's practical?

Algebra Level 5

25(4a12+1)(4a22+1)(4a52+1) 25(4a_1^2 + 1)(4a_2^2 + 1)\cdots (4a_{5}^2 + 1)

Let a1,a2,,a5a_1, a_2, \ldots,a_{5} denote the roots to the equation m=15mxm=0 \displaystyle \sum_{m=1}^{5} m x^m = 0 .

Find the value of the expression above.

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