AMC 12A 2017 Problem 23

For certain real numbers a, b, and c, the polynomial

g(x)=x^{3}+a x^{2}+x+10

has three distinct roots, and each root of g(x) is also a root of the polynomial

f(x)=x^{4}+x^{3}+b x^{2}+100 x+c

What is f(1) ?

Answer Choices
A. -9009
B. -8008
C. -7007
D. -6006
E. -5005