Find roots of polynomial $$ p(x) = x^4+x^3+5x^2+\frac{3433333}{10000}x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.0117\\[1 em]x_2 &= -7.0984\\[1 em]x_3 &= 3.055+6.2471i\\[1 em]x_4 &= 3.055-6.2471i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 10000 } $.
$$ \begin{aligned} x^4+x^3+5x^2+\frac{3433333}{10000}x+4 & = 0 ~~~ / \cdot \color{blue}{ 10000 } \\[1 em] 10000x^4+10000x^3+50000x^2+3433333x+40000 & = 0 \end{aligned} $$Step 2:
Polynomial $ 10000x^4+10000x^3+50000x^2+3433333x+40000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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