2008 AMC 10B Problem 9 — Solution | LIVE by Po-Shen Loh

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2008 AMC 10B Problem 9

Attempt Problem 9 of the 2008 AMC 10B 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 2008 AMC 10B solutions, or check the answer key.

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

9.

A quadratic equation $ax^2-2ax+b=0$ has two real solutions. What is the average of the solutions?

$1$

$2$

$\dfrac{b}{a}$

$\dfrac{2b}{a}$

$\sqrt{2a-b}$

Answer: A

Concepts:Vieta’s Formulas quadratic

Difficulty rating: 1040

Solution:

By Vieta's formulas, the sum of the roots of $ax^2-2ax+b=0$ is $\dfrac{-(-2a)}{a}=2.$

The average is half of this, namely $1.$

Thus, the correct answer is A.

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