Roots, abcde

Algebra Level 3

Let \(a,b,c,d,e\) be the roots (of \(x\)) of the equation \(2x^5 - 2x^4 + 32x^3 - mx^2 + nx + 8 = 0 \), where \(m\) and \(n\) are unknown constants.

Find the numerical value of \(E = a^2bcde + ab^2cde +abc^2de + abcd^2e + abcde^2 \).

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