Find roots of polynomial $$ p(x) = -2s^5-370s^3-58s^4-1100s^2-3600s-88000 $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= -21.6517\\[1 em]s_2 &= 2.8082+4.6232i\\[1 em]s_3 &= 2.8082-4.6232i\\[1 em]s_4 &= -6.4823+5.2375i\\[1 em]s_5 &= -6.4823-5.2375i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} -2s^5-370s^3-58s^4-1100s^2-3600s-88000 & = 0\\[1 em] -2s^5-58s^4-370s^3-1100s^2-3600s-88000 & = 0 \end{aligned} $$Step 2:
Polynomial $ -2s^5-58s^4-370s^3-1100s^2-3600s-88000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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