Question
$$x^3+\frac{1}{2}x^2+\frac{5}{3} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^3+\frac{1}{2}x^2+\frac{5}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6x^3+6 \cdot \frac{1}{2}x^2+6\cdot\frac{5}{3} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]6x^3+3x^2+10 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Equations Solver