Question
$$x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}-282 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}-282 &= 0&& \text{simplify left side} \\[1 em]x^{10}+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x-282 &= 0&& \\[1 em] \end{aligned} $$
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