Question
$$x^4+x^3+x^2+x^1+1 = 750 \cdot \frac{x^{31}}{11}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^4+x^3+x^2+x^1+1 &= 750 \cdot \frac{x^{31}}{11}&& \text{multiply ALL terms by } \color{blue}{ 11 }. \\[1 em]11x^4+11x^3+11x^2+11x^1+11\cdot1 &= 11\cdot750 \cdot \frac{x^{31}}{11}&& \text{cancel out the denominators} \\[1 em]11x^4+11x^3+11x^2+11x+11 &= 750x^{31}&& \text{move all terms to the left hand side } \\[1 em]11x^4+11x^3+11x^2+11x+11-750x^{31} &= 0&& \text{simplify left side} \\[1 em]-750x^{31}+11x^4+11x^3+11x^2+11x+11 &= 0&& \\[1 em] \end{aligned} $$
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