2013 AMC 10B Problem 19

The real numbers c,b,a form an arithmetic sequence with a\ge b\ge c\ge 0. The quadratic ax^2+bx+c has exactly one root. What is this root?

\textbf{(A)}\ -7-4\sqrt{3}\qquad\textbf{(B)}\ -2-\sqrt{3}\qquad\textbf{(C)}\ -1\qquad\textbf{(D)}\ -2+\sqrt{3}\qquad\textbf{(E)}\ -7+4\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.