Difference between revisions of "1985 OIM Problems/Problem 3"
| Line 3: | Line 3: | ||
<cmath>4x^4-ax^3+bx^2-cs+5=0</cmath> | <cmath>4x^4-ax^3+bx^2-cs+5=0</cmath> | ||
knowing that they're all real, positives and that: | knowing that they're all real, positives and that: | ||
| − | <cmath>frac{r_1}{2}+frac{r_2}{4}+frac{r_3}{5}+frac{r_4}{8}=1</cmath> | + | <cmath>\frac{r_1}{2}+\frac{r_2}{4}+\frac{r_3}{5}+\frac{r_4}{8}=1</cmath> |
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 12:34, 13 December 2023
Problem
Find the roots 
, 
, 
, and 
of the equation:
![\[4x^4-ax^3+bx^2-cs+5=0\]](http://latex.artofproblemsolving.com/1/4/b/14b39122ebaa1ff2cdaa7038e6f436bc8fa02025.png)
knowing that they're all real, positives and that:
![\[\frac{r_1}{2}+\frac{r_2}{4}+\frac{r_3}{5}+\frac{r_4}{8}=1\]](http://latex.artofproblemsolving.com/d/1/9/d195dc3007c6d7345fb00b1bdacae607e880987d.png)
Solution
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