Find roots of polynomial $$ p(x) = x^5+x^4+8x^3+10x^2+80x+32 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4146\\[1 em]x_2 &= -1.7202+2.3602i\\[1 em]x_3 &= -1.7202-2.3602i\\[1 em]x_4 &= 1.4274+2.6481i\\[1 em]x_5 &= 1.4274-2.6481i \end{aligned} $$Explanation
Polynomial $ x^5+x^4+8x^3+10x^2+80x+32 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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