2001 AMC 12 Problems/Problem 19
Problem
The polynomial has the property that the average of its zeros, the product of its zeros, and the sum of its coefficients are all equal. The -intercept of the graph of is 2. What is ?
Solution
We are given . So the product of the roots is by Vieta's formulas. These also tell us that is the average of the zeros, so . We are also given that the sum of the coefficients is , so . So the answer is .
Video Solution by OmegaLearn
https://youtu.be/czk6OsfrbxQ?t=678
~ pi_is_3.14
Video Solution
https://www.youtube.com/watch?v=qtlXAxj4y2Y
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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All AMC 12 Problems and Solutions |
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