AMC 12A 2019 Problem 14

For a certain complex number c, the polynomial

P(x)=\left(x^{2}-2 x+2\right)\left(x^{2}-c x+4\right)\left(x^{2}-4 x+8\right)

has exactly 4 distinct roots. What is |c| ?

Answer Choices
A. 2
B. \sqrt{6}
C. 2 \sqrt{2}
D. 3
E. \sqrt{10}