Difference between revisions of "2003 AIME II Problems/Problem 9"
m (add problem) |
m |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | + | Consider the polynomials <math>P(x) = x^{6} - x^{5} - x^{3} - x^{2} - x</math> and <math>Q(x) = x^{4} - x^{3} - x^{2} - 1.</math> Given that <math>z_{1},z_{2},z_{3},</math> and <math>z_{4}</math> are the roots of <math>Q(x) = 0,</math> find <math>P(z_{1}) + P(z_{2}) + P(z_{3}) + P(z_{4}).</math> | |
| + | |||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2003|n=II|num-b=8|num-a=10}} | |
| − | |||
| − | |||
| − | |||
| − | |||
Revision as of 14:39, 21 November 2007
Problem
Consider the polynomials 
and 
Given that 
and 
are the roots of 
find 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 | ||
