MathNet 2022-part-04 — 197 problems (EN–VI) Question 61

Suppose that the polynomial $P(x) = x^{3} + 4x^{2} + bx + c$ has a single root $r$ and a double root $s$ for some distinct real numbers $r$ and $s$. Given that $P(-2s) = 324$, what is the sum of all possible values of $|c|$?