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Algebra Level 5

\[1 x^1 + 2x^2 + 3x^3 + 4x^4 + 5x^5 = 0 \]

Let \(a_1, a_2, \ldots,a_{5} \) denote the roots to the above equation. Find the value:

\[(4{ a }_{ 1 }+1)(4a_{ 2 }+1)\cdots (4a_{ 5 }+1)\]


Inspiration.

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