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2013 AMC 10B Question 19

AMC10 · 2013 AMC 10B

Question 19

The real numbers $c,$ $b,$ $a$ form an arithmetic sequence with $a \geq b \geq c \geq 0.$ The quadratic $ax^2+bx+c$ has exactly one root. What is this root?
  1. $ -7-4\sqrt{3} $
  2. $ -2-\sqrt{3} $
  3. $ -1 $
  4. $ -2+\sqrt{3} $
  5. $ -7+4\sqrt{3} $