2014 AMC 12B Problems/Problem 16
Contents
Problem
Let be a cubic polynomial with , , and . What is ?
Solution
Let . Plugging in for , we find , and plugging in and for , we obtain the following equations: Adding these two equations together, we get If we plug in and in for , we find that Multiplying the third equation by and adding gives us our desired result, so
Solution 2
If we use Gregory's Triangle, the following happens:
Since this is cubic, the common difference is for the linear level so the string of s are infinite in each direction. If we put a on each side of the original , we can solve for and .
The above shows us that is and is so .
See also
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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All AMC 12 Problems and Solutions |
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