Difference between revisions of "1985 OIM Problems/Problem 3"
(Created page with "== Problem == Find the roots <math>r_1</math>, <math>r_2</math>, <math>r_3</math>, and <math>r_4</math> of the equation: <cmath>4x^4-ax^3+bx^2-cs+5=0</cmath> knowing that the...") |
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| 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> |
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 12:33, 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/a/2/f/a2f8ef4a2914cebde5515cce95e5c2d70975f19d.png)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
