Difference between revisions of "2002 AMC 12A Problems/Problem 1"
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− | {{duplicate|[[2002 AMC 12A Problems| | + | {{duplicate|[[2002 AMC 12A Problems|2002 AMC 12A #1]] and [[2002 AMC 10A Problems|2002 AMC 10A #10]]}} |
== Problem == | == Problem == |
Revision as of 14:32, 18 February 2009
- The following problem is from both the 2002 AMC 12A #1 and 2002 AMC 10A #10, so both problems redirect to this page.
Contents
[hide]Problem
Compute the sum of all the roots of
Solution
Solution 1
We expand to get which is after combining like terms. Using the quadratic part of Vieta's Formulas, we find the sum of the roots is .
Solution 2
Combine terms to get , hence the roots are and , thus our answer is .
See also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by First Question |
Followed by Problem 2 |
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 12 Problems and Solutions |
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 |