Question
$$10000 = \frac{24673}{100}x^4-\frac{17391}{10}x^3+\frac{49165}{10}x^2-\frac{44716}{10}x+\frac{59198}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10000 &= \frac{24673}{100}x^4-\frac{17391}{10}x^3+\frac{49165}{10}x^2-\frac{44716}{10}x+\frac{59198}{10}&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot10000 &= 100 \cdot \frac{24673}{100}x^4-100\frac{17391}{10}x^3+100\frac{49165}{10}x^2-100\frac{44716}{10}x+100\cdot\frac{59198}{10}&& \text{cancel out the denominators} \\[1 em]1000000 &= 24673x^4-173910x^3+491650x^2-447160x+591980&& \text{move all terms to the left hand side } \\[1 em]1000000-24673x^4+173910x^3-491650x^2+447160x-591980 &= 0&& \text{simplify left side} \\[1 em]-24673x^4+173910x^3-491650x^2+447160x+408020 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver