Difference between revisions of "2008 AMC 10B Problems/Problem 9"

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==Problem==
 
==Problem==
A uadratic equation ax^2 - 2ax + b = 0 has two real solutions. What is the average of these two solutions?
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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  
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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 (ProblemsAnswer KeyResources)
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
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