Find roots of polynomial $$ p(x) = z^4+\frac{1}{625} $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 0.1414+0.1414i\\[1 em]z_2 &= 0.1414-0.1414i\\[1 em]z_3 &= -0.1414+0.1414i\\[1 em]z_4 &= -0.1414-0.1414i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 625 } $.
$$ \begin{aligned} z^4+\frac{1}{625} & = 0 ~~~ / \cdot \color{blue}{ 625 } \\[1 em] 625z^4+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ 625z^4+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
This page was created using
Polynomial Roots Calculator