Find roots of polynomial $$ p(x) = x^4+x^3+5x^2+\frac{3433}{100}x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.1185\\[1 em]x_2 &= -2.9999\\[1 em]x_3 &= 1.0592+3.1825i\\[1 em]x_4 &= 1.0592-3.1825i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} x^4+x^3+5x^2+\frac{3433}{100}x+4 & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 100x^4+100x^3+500x^2+3433x+400 & = 0 \end{aligned} $$Step 2:
Polynomial $ 100x^4+100x^3+500x^2+3433x+400 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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