2003 AMC 10A Problems/Problem 18
Contents
Problem
What is the sum of the reciprocals of the roots of the equation
?
Solution 1
Multiplying both sides by :
Let the roots be and
.
The problem is asking for
By Vieta's formulas:
So the answer is .
Solution 2
Dividing both sides by ,
, we see by Vieta's formulas that the sum of the roots is
.
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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All AMC 10 Problems and Solutions |
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