2020 AMC 10A Problem 5

Attempt Problem 5 of the 2020 AMC 10A below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10A solutions, or check the answer key.

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

What is the sum of all real numbers $x$ for which $|x^2-12x+34|=2?$

$12$

$15$

$18$

$21$

$25$

Answer: C

Concepts:absolute value quadratic

Difficulty rating: 1020

Video solution:

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Written solution:

The equation means $x^2-12x+34=2$ or $x^2-12x+34=-2$ . The first gives $x^2-12x+32=0$ , with roots $4$ and $8$ . The second gives $(x-6)^2=0$ , with root $6$ . The sum of all real solutions is $4+8+6=18$ . Thus, C is the correct answer.

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