Descartes' Rule Of Sign Is Not Enough!

Algebra Level 4

\[ \large { x }^{ 6 }-12{ x }^{ 5 }+a{ x }^{ 4 }+b{ x }^{ 3 }+c{ x }^{ 2 }+dx+64 =0 \]

Let \(a,b,c,d\) be all constants.

If all of the roots of the above equation are positive, find \(b + c - a\).

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