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2008 AMC 10B Problem 9

Problem 9 of 25EasierAlgebra

A quadratic equation ax2−2ax+b=0ax^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 ax2−2ax+b=0ax^2-2ax+b=0 is −(−2a)a=2.\dfrac{-(-2a)}{a}=2. The average is half of this, namely 1.1. Thus, the correct answer is A.
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Tagged: Vieta’s Formulas · quadratic

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