Difference between revisions of "1984 USAMO Problems/Problem 1"
5849206328x (talk | contribs) |
|||
| Line 34: | Line 34: | ||
{{USAMO box|year=1984|before=First<br>Problem|num-a=2}} | {{USAMO box|year=1984|before=First<br>Problem|num-a=2}} | ||
| + | {{MAA Notice}} | ||
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Revision as of 18:15, 3 July 2013
Problem
In the polynomial 
, the product of 
of its roots is 
. Find 
.
Solution
Let the four roots be 
. By Vieta's Formulas, we have the following:
*
*
Substituting given values obtains the following:
Multiplying the * equation by 16 gives
. Adding it to the previous equation gives
See Also
| 1984 USAMO (Problems • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
