Difference between revisions of "2012 AIME I Problems/Problem 14"
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==Problem 14== | ==Problem 14== | ||
| + | Complex numbers <math>a,</math> <math>b,</math> and <math>c</math> are zeros of a polynomial <math>P(z) = z^3 + qz + r,</math> and <math>|a|^2 + |b|^2 + |c|^2 = 250.</math> The points corresponding to <math>a,</math> <math>b,</math> and <math>c</math> in the complex plane are the vertices of a right triangle with hypotenuse <math>h.</math> Find <math>h^2.</math> | ||
== Solution == | == Solution == | ||
Revision as of 01:37, 17 March 2012
Problem 14
Complex numbers 
and 
are zeros of a polynomial 
and 
The points corresponding to and in the complex plane are the vertices of a right triangle with hypotenuse 
Find 
Solution
See also
| 2012 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
