MathDB

10

Part of 2005 AMC 10

Problems(2)

Quadratic with one solution

Source:

11/7/2005
There are two values of a a for which the equation 4x^2 \plus{} ax \plus{} 8x \plus{} 9 \equal{} 0 has only one solution for x x. What is the sum of these values of a a? (A)\ \minus{}16\qquad (B)\ \minus{}8\qquad (C)\ 0\qquad (D)\ 8\qquad (E)\ 20
quadratics
Point D and triangle ABC

Source:

11/17/2005
In △ABC \triangle ABC, we have AC \equal{} BC \equal{} 7 and AB \equal{} 2. Suppose that D D is a point on line AB AB such that B B lies between A A and D D and CD \equal{} 8. What is BD BD? <spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 42 <span class='latex-bold'>(A)</span>\ 3\qquad <span class='latex-bold'>(B)</span>\ 2 \sqrt {3}\qquad <span class='latex-bold'>(C)</span>\ 4\qquad <span class='latex-bold'>(D)</span>\ 5\qquad <span class='latex-bold'>(E)</span>\ 4 \sqrt {2}
Pythagorean Theoremgeometry