Question
$$x^4+x^3+x^2+x = 4+\frac{356439}{1000000}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^4+x^3+x^2+x &= 4+\frac{356439}{1000000}&& \text{multiply ALL terms by } \color{blue}{ 1000000 }. \\[1 em]1000000x^4+1000000x^3+1000000x^2+1000000x &= 1000000\cdot4+1000000\cdot\frac{356439}{1000000}&& \text{cancel out the denominators} \\[1 em]1000000x^4+1000000x^3+1000000x^2+1000000x &= 4000000+356439&& \text{simplify right side} \\[1 em]1000000x^4+1000000x^3+1000000x^2+1000000x &= 4356439&& \text{move all terms to the left hand side } \\[1 em]1000000x^4+1000000x^3+1000000x^2+1000000x-4356439 &= 0&& \\[1 em] \end{aligned} $$
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