2002 AMC 10A Problem 10

Attempt Problem 10 of the 2002 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

Compute the sum of all the roots of

(2x+3)(x-4)

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

\dfrac{7}{2}

4

5

7

13

Factor out the common

(2x+3)

Combine

(x-4)+(x-6)

inside the bracket

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.

Problem 10 in other years