Question
$$10000 = \frac{2111}{10}x^4-\frac{16866}{10}x^3+\frac{51341}{10}x^2-\frac{55232}{10}x+\frac{54766}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10000 &= \frac{2111}{10}x^4-\frac{16866}{10}x^3+\frac{51341}{10}x^2-\frac{55232}{10}x+\frac{54766}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot10000 &= 10 \cdot \frac{2111}{10}x^4-10\frac{16866}{10}x^3+10\frac{51341}{10}x^2-10\frac{55232}{10}x+10\cdot\frac{54766}{10}&& \text{cancel out the denominators} \\[1 em]100000 &= 2111x^4-16866x^3+51341x^2-55232x+54766&& \text{move all terms to the left hand side } \\[1 em]100000-2111x^4+16866x^3-51341x^2+55232x-54766 &= 0&& \text{simplify left side} \\[1 em]-2111x^4+16866x^3-51341x^2+55232x+45234 &= 0&& \\[1 em] \end{aligned} $$
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