Less than four distinct roots

Algebra Level 5

Find the sum of all (distinct) complex values of \(c\) for which the polynomial \[f_c(x)=x^4-(c^2-7c+11)x^2+(18-21c+8c^2-c^3)\] has strictly less than four distinct complex zeroes.

Details and assumptions

The real numbers are a subset of the complex numbers.

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