NMTC 2015 Final Q5

Algebra Level 3

\[\begin{eqnarray} a + b + c + d + e + f& = &1\\ -a + b - c + d - e + f& = &-1 \\ 5a + 4b + 3c + 2d + e& =&0 \\ 5a - 4b + 3c - 2d + e& = 0 \\ 20a + 12b + 6c + 2d& = &0 \\ -20a + 12b - 6c + 2d& = &0 \end{eqnarray}\].

Find \(abcdef\)

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