Question
$$x^2+x^4-3x^6+x^5+10 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^2+x^4-3x^6+x^5+10 &= 0&& \text{simplify left side} \\[1 em]-3x^6+x^5+x^4+x^2+10 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver