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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