Find roots of polynomial $$ p(x) = n^4+2n^3+9n^2+8n+16 $$
Answer
The roots of polynomial $ p(n) $ are:
$$ \begin{aligned}n_1 &= -0.5+1.9365i\\[1 em]n_2 &= -0.5-1.9365i\\[1 em]n_3 &= -0.5+1.9365i\\[1 em]n_4 &= -0.5-1.9365i \end{aligned} $$Explanation
Polynomial $ n^4+2n^3+9n^2+8n+16 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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