Less than four distinct roots

Algebra Level 5

Find the sum of all (distinct) complex values of cc for which the polynomial fc(x)=x4(c27c+11)x2+(1821c+8c2c3)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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