2002 AMC 12A Problems/Problem 1

Problem

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

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

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

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

2002 AMC 12A (Problems • Answer Key • Resources)
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