Find roots of polynomial $$ p(x) = x^4-\frac{803}{4227966}x^2+\frac{803}{4227966} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.0833+0.0827i\\[1 em]x_2 &= 0.0833-0.0827i\\[1 em]x_3 &= -0.0833+0.0827i\\[1 em]x_4 &= -0.0833-0.0827i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4227966 } $.
$$ \begin{aligned} x^4-\frac{803}{4227966}x^2+\frac{803}{4227966} & = 0 ~~~ / \cdot \color{blue}{ 4227966 } \\[1 em] 4227966x^4-803x^2+803 & = 0 \end{aligned} $$Step 2:
Polynomial $ 4227966x^4-803x^2+803 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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