2008 AMC 10B Problems/Problem 9

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Problem

A quadratic equation ax^2 - 2ax + b = 0 has two real solutions. What is the average of these two solutions? A) 1 B) 2 C) b/a D) 2b/a

Solution

Dividing both sides by a, we get x^2 - 2x + b/a - 0. By Vieta's formulas, the sum of the roots is 2, therefore their average is 1 (A).

See also

2008 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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All AMC 10 Problems and Solutions
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