Difference between revisions of "2013 AMC 10B Problems/Problem 19"

Revision as of 20:04, 21 February 2013

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?

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

@@ Line 1: / Line 1: @@
-The real numbers<math>c,b,a</math> form an arithmetic sequence with <math>a\ge b\ge c\ge 0</math> The quadratic <math>ax^2+bx+c</math> has exactly one root. What is this root?
+==Problem==
+The real numbers <math>c,b,a</math> form an arithmetic sequence with <math>a\ge b\ge c\ge 0</math> The quadratic <math>ax^2+bx+c</math> has exactly one root. What is this root?
 <math> \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} </math>