2010 AMC 12A Problems/Problem 21
Problem
The graph of lies above the line except at three values of , where the graph and the line intersect. What is the largest of these values?
Solution
The values in which intersect at are the same as the zeros of .
Since there are zeros and the function is never negative, all zeros must be double roots because the function's degree is .
Suppose we let , , and be the roots of this function, and let be the cubic polynomial with roots , , and .
In order to find we must first expand out the terms of .
[Quick note: Since we don't know , , and , we really don't even need the last 3 terms of the expansion.]
All that's left is to find the largest root of .
See also
2010 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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All AMC 12 Problems and Solutions |
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