2019 AMC 12A Problems/Problem 17
Contents
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 Sums we get the answer as 10
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.
See Also
2019 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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