Find roots of polynomial $$ p(x) = 5s^4+2s^3+\frac{64}{100}s^2+\frac{8}{100}s-\frac{12}{1000} $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 0.0812\\[1 em]s_2 &= -0.2688\\[1 em]s_3 &= -0.1062+0.3142i\\[1 em]s_4 &= -0.1062-0.3142i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 1000 } $.
$$ \begin{aligned} 5s^4+2s^3+\frac{64}{100}s^2+\frac{8}{100}s-\frac{12}{1000} & = 0 ~~~ / \cdot \color{blue}{ 1000 } \\[1 em] 5000s^4+2000s^3+640s^2+80s-12 & = 0 \end{aligned} $$Step 2:
Polynomial $ 5000s^4+2000s^3+640s^2+80s-12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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