$$\frac{-5k^2+k^3+8k+4}{-1+k} = 0$$
Answer
$$ \begin{matrix}k_1 = -0.39486 & k_2 = 2.69743+1.6894i & k_3 = 2.69743-1.6894i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{-5k^2+k^3+8k+4}{-1+k} &= 0&& \text{multiply ALL terms by } \color{blue}{ -1+k }. \\[1 em](-1+k)\frac{-5k^2+k^3+8k+4}{-1+k} &= (-1+k)\cdot0&& \text{cancel out the denominators} \\[1 em]-5k^2+k^3+8k+4 &= 0&& \text{simplify left side} \\[1 em]k^3-5k^2+8k+4 &= 0&& \\[1 em] \end{aligned} $$
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