Problematic polynomial

Algebra Level 5

\[\large f\left( x \right) =4{ x }^{ 6 }+3{ x }^{ 4 }+2{ x }^{ 3 }+7\]

If \(f(x)\) is polynomial having roots \({ r }_{ i }\) for \(i\) equal to \(1\) to \(6\).Then find the value of \( \displaystyle \sum _{ k=1 }^{ 6 }{ { { \left( \frac { \prod { { r }_{ i } } }{ { r }_{ k } } \right) }^{ 4 } } } \). Give your answer to 3 decimal places.

This problem is original.
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