2008 AMC 10B Problems/Problem 9
Contents
[hide]Problem
A quadratic equation has two real solutions. What is the average of these two solutions?
Solution 1
Dividing both sides by , we get . By Vieta's formulas, the sum of the roots is , therefore their average is .
Solution 2
We know that for an equation , the sum of the roots is . This means that the sum of the roots for is , or . The average is the sum of the two roots divided by two, so the average is .
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AMC 10 Problems and Solutions |
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