Difference between revisions of "1989 USAMO Problems/Problem 3"
(New page: ==Problem== Let <math>P(z)= z^n + c_1 z^{n-1} + c_2 z^{n-2} + \cdots + c_n</math> be a polynomial in the complex variable <math>z</math>, with real coefficients <math>c_k</math>. Suppose t...) |
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Revision as of 12:24, 8 October 2007
Problem
Let 
be a polynomial in the complex variable 
, with real coefficients 
. Suppose that 
. Prove that there exist real numbers 
and 
such that 
and 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1989 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
