2019 AMC 12A Problems/Problem 17
Contents
[hide]Problem
Let denote the sum of the th powers of the roots of the polynomial . In particular, , , and . Let , , and be real numbers such that for , , What is ?
Solution 1
Applying Newton's Sums (see this link), we get the answer as .
Solution 2
Let , and be the roots of the polynomial. Then,
Adding these three equations, we get
can be written as .
We are given that is satisfied for , , , meaning it must be satisfied when , giving us .
Therefore, , and by matching coefficients.
.
Video Solution
For those who want a video solution: https://www.youtube.com/watch?v=tAS_DbKmtzI
See Also
2019 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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