For certain real numbers a, b, and c, the polynomial g(x)=x3+ax2+x+10 has three distinct roots, and each root of g(x) is also a root of the polynomial f(x)=x4+x3+bx2+100x+c. What is f(1)?<spanclass=′latex−bold′>(A)</span>−9009<spanclass=′latex−bold′>(B)</span>−8008<spanclass=′latex−bold′>(C)</span>−7007<spanclass=′latex−bold′>(D)</span>−6006<spanclass=′latex−bold′>(E)</span>−5005