2000 AMC 12 Problems/Problem 22
Contents
[hide]Problem
The graph below shows a portion of the curve defined by the quartic polynomial . Which of the following is the smallest?
Solution
Note that there are 3 maxima/minima. Hence we know that the rest of the graph is greater than 10. We approximate each of the above expressions:
- According to the graph,
- The product of the roots is by Vieta’s formulas. Also, according to the graph.
- The product of the real roots is , and the total product is (from above), so the product of the non-real roots is .
- The sum of the coefficients is
- The sum of the real roots is .
Clearly is the smallest.
Video Solution
See Also
2000 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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