Find roots of polynomial $$ p(x) = -2s^2-370s^3-58s^4-1100s^2-3600s-88000 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 2.661+4.6877i\\[1 em]s_2 &= 2.661-4.6877i\\[1 em]s_3 &= -5.8507+4.2414i\\[1 em]s_4 &= -5.8507-4.2414i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{-2s^2} -370s^3-58s^4 \color{blue}{-1100s^2} -3600s-88000 = -58s^4-370s^3 \color{blue}{-1102s^2} -3600s-88000 $$Step 2:
Polynomial $ -58s^4-370s^3-1102s^2-3600s-88000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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