2008 AMC 10B Problem 9

Problem 9 of 25EasierAlgebra

A quadratic equation

ax^2-2ax+b=0

has two real solutions. What is the average of the solutions?

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Solution

By Vieta’s formulas, the sum of the roots of

ax^2-2ax+b=0

\dfrac{-(-2a)}{a}=2.

The average is half of this, namely

1.

Thus, the correct answer is A.

Concepts: Vieta’s Formulas · quadratic

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