Complex sum

Algebra Level 4

\[{ f }_{ c }(x)={ x }^{ 4 }-({ c }^{ 2 }-7c+11){ x }^{ 2 }+(18-21c+8{ c }^{ 2 }-{ c }^{ 3 })\]

Find the sum of all (distinct) complex values of \(c\) for which the polynomial has strictly less than four distinct complex zeroes.

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