Question
$$10000 = \frac{7788}{100}x^5-\frac{13985}{10}x^4+\frac{92305}{10}x^3-\frac{26448}{1}x^2+\frac{311156}{1}x-\frac{81783}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 10000 &= \frac{7788}{100}x^5-\frac{13985}{10}x^4+\frac{92305}{10}x^3-\frac{26448}{1}x^2+\frac{311156}{1}x-\frac{81783}{10}&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot10000 &= 100 \cdot \frac{7788}{100}x^5-100\frac{13985}{10}x^4+100\frac{92305}{10}x^3-100\frac{26448}{1}x^2+100\frac{311156}{1}x-100\cdot\frac{81783}{10}&& \text{cancel out the denominators} \\[1 em]1000000 &= 7788x^5-139850x^4+923050x^3-2644800x^2+31115600x-817830&& \text{move all terms to the left hand side } \\[1 em]1000000-7788x^5+139850x^4-923050x^3+2644800x^2-x+817830 &= 0&& \text{simplify left side} \\[1 em]-7788x^5+139850x^4-923050x^3+2644800x^2-x+1817830 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver