Question
$$1-x+\frac{1}{10}x^2+\frac{1}{20}x^3 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 1-x+\frac{1}{10}x^2+\frac{1}{20}x^3 &= 0&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot1-20x+20 \cdot \frac{1}{10}x^2+20\frac{1}{20}x^3 &= 20\cdot0&& \text{cancel out the denominators} \\[1 em]20-20x+2x^2+x^3 &= 0&& \text{simplify left side} \\[1 em]x^3+2x^2-20x+20 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver