Difference between revisions of "2008 AMC 10B Problems/Problem 9"
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==Problem== | ==Problem== | ||
| − | A | + | 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 | + | A) 1 B) 2 C) b/a D) 2b/a |
==Solution== | ==Solution== | ||
Revision as of 13:02, 25 January 2009
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 (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 | ||
