2008 AMC 10B Problems/Problem 9
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 . The average is the sum of the two roots divided by two, so the average is .
Solution 3
Using the quadratic formula(assuming ),we get . Let . Simplifying, we get . That means the sum of the solutions is , so the average is .
~idk12345678
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.