2002 AMC 10A Problem 10 — Solution | LIVE by Po-Shen Loh

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2002 AMC 10A Problem 10

Below is the professionally curated solution for Problem 10 of the 2002 AMC 10A, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:quadratic factoring

Difficulty rating: 1120

10.

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

$\dfrac{7}{2}$

$4$

$5$

$7$

$13$

Solution:

Factoring, $(2x+3)\left[(x-4)+(x-6)\right]=(2x+3)(2x-10)=0.$

The roots are $-\dfrac{3}{2}$ and $5,$ which sum to $\dfrac{7}{2}.$

Thus, the correct answer is A.

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