2002 AMC 10A Problem 10

Problem 10 of 25EasierAlgebra

Compute the sum of all the roots of

(2x+3)(x-4)

+(2x+3)(x-6)=0.

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Solution

Factoring,

\begin{gathered} (2x+3)\left[(x-4)+(x-6)\right] \\ = (2x+3)(2x-10) \\ = 0. \end{gathered}

The roots are

-\dfrac{3}{2}

and

5,

which sum to

\dfrac{7}{2}.

Thus, the correct answer is A.

Concepts: quadratic · factoring

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.