Difference between revisions of "1985 OIM Problems/Problem 3"
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== Problem == | == Problem == | ||
Find the roots <math>r_1</math>, <math>r_2</math>, <math>r_3</math>, and <math>r_4</math> of the equation: | 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- | + | <cmath>4x^4-ax^3+bx^2-cx+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> | ||
Revision as of 11:34, 13 December 2023
Problem
Find the roots 
, 
, 
, and 
of the equation:
![\[4x^4-ax^3+bx^2-cx+5=0\]](http://latex.artofproblemsolving.com/d/9/3/d93275ae96fdc4e2a22e121aab01b3fc03049a4e.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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