Question
$$10000 = \frac{8592}{10000}x^4+\frac{7172}{10}x^3-\frac{37363}{10}x^2+\frac{65944}{10}x+\frac{36068}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10000 &= \frac{8592}{10000}x^4+\frac{7172}{10}x^3-\frac{37363}{10}x^2+\frac{65944}{10}x+\frac{36068}{10}&& \text{multiply ALL terms by } \color{blue}{ 10000 }. \\[1 em]10000\cdot10000 &= 10000 \cdot \frac{8592}{10000}x^4+10000\frac{7172}{10}x^3-10000\frac{37363}{10}x^2+10000\frac{65944}{10}x+10000\cdot\frac{36068}{10}&& \text{cancel out the denominators} \\[1 em]100000000 &= 8592x^4+7172000x^3-37363000x^2+65944000x+36068000&& \text{move all terms to the left hand side } \\[1 em]100000000-8592x^4-7172000x^3+x^2-x-36068000 &= 0&& \text{simplify left side} \\[1 em]-8592x^4-7172000x^3+x^2-x+63932000 &= 0&& \\[1 em] \end{aligned} $$
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