AMC 12A 2010 Problem 21

The graph of y=x^{6}-10 x^{5}+29 x^{4}-4 x^{3}+a x^{2} lies above the line y=b x+c except at three values of x, where the graph and the line intersect. What is the largest of those values?

Answer Choices
A. 4
B. 5
C. 6
D. 7
E. 8