Difference between revisions of "1983 USAMO"
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==Problem 1== | ==Problem 1== | ||
If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three? | If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three? | ||
| + | |||
| + | ==Problem 2== | ||
| + | Prove that the zeros of | ||
| + | |||
| + | <cmath>x^5+ax^4+bx^3+cx^2+dx+e=0</cmath> | ||
| + | |||
| + | cannot all be real if <math>2a^2<5b</math>. | ||
Revision as of 18:02, 13 November 2011
Problem 1
If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three?
Problem 2
Prove that the zeros of
![\[x^5+ax^4+bx^3+cx^2+dx+e=0\]](http://latex.artofproblemsolving.com/9/0/4/9049ba78fdefb11bd3a89101dac429cad1017dce.png)
cannot all be real if 
.
