2003 AMC 10A Problems/Problem 5
Contents
[hide]Problem
Let and denote the solutions of . What is the value of ?
Solutions
Solution 1
Using factoring:
or
So and are and .
Therefore the answer is
Solution 2
We can use the sum and product of a quadratic (a.k.a Vieta):
Solution 3
By inspection, we quickly note that is a solution to the equation, therefore the answer is
Solution 4
The form resembles the factored form for the quadratic, namely based on the information given. Note putting in 1 for in the that quadratic immediately yields the desired expression. Thus,
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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All AMC 10 Problems and Solutions |
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