# 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.