2003 AIME II Problems/Problem 9
Problem
Consider the polynomials and
Given that
and
are the roots of
find
Solution
therefore
therefore
Also
So $$ (Error compiling LaTeX. Unknown error_msg)z_1^6-z_1^5-z_1^4=z_1^2$$ (Error compiling LaTeX. Unknown error_msg)
So in
Since and
can now be
Now this also follows for all roots of
Now
Now by Vieta's we know that
So by Newton Sums we can find
So finally
See also
2003 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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