$$25k^5+5k^3 = 0$$
Answer
$$ \begin{matrix}k_1 = 0 & k_2 = \dfrac{\sqrt{ 5 }}{ 5 } i & k_3 = - \dfrac{\sqrt{ 5 }}{ 5 } i \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 25x^{5}+5x^{3} = 0 } $, first we need to factor our $ x^3 $.
$$ 25x^{5}+5x^{3} = x^3 \left( 25x^{2}+5 \right) $$$ x = 0 $ is a root of multiplicity $ 3 $.
The remaining roots can be found by solving equation $ 25x^{2}+5 = 0$.
$ 25x^{2}+5 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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