Difference between revisions of "2002 AMC 12A Problems/Problem 1"

(Solution)
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== Problem ==
 
== Problem ==
 
Compute the sum of all the roots of
 
Compute the sum of all the roots of
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The sum of the roots is therefore
 
The sum of the roots is therefore
  
<math>5-\dfrac{3}{2}=\dfrac{7}{2} \Rightarrow \mathrm {(B)}</math>
+
<math>5-\dfrac{3}{2}=\dfrac{7}{2} \Rightarrow \mathrm {(A)}</math>
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2002|ab=A|before=First Question|num-a=2}}
 
{{AMC12 box|year=2002|ab=A|before=First Question|num-a=2}}

Revision as of 15:25, 24 December 2007

Problem

Compute the sum of all the roots of $(2x+3)(x-4)+(2x+3)(x-6)=0$

$\mathrm{(A) \ } \frac{7}{2}\qquad \mathrm{(B) \ } 4\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 13$

Solution

That is equal to $(2x+3)(2x-10)=0$

We can divide out by 4 to get

$(x+\frac{3}{2})(x-5)=0$

The sum of the roots is therefore

$5-\dfrac{3}{2}=\dfrac{7}{2} \Rightarrow \mathrm {(A)}$

See also

2002 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First Question
Followed by
Problem 2
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All AMC 12 Problems and Solutions