Find roots of polynomial $$ p(x) = x^5+8x^4+12x^3+18x^2+80x+51 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7234\\[1 em]x_2 &= -2.5949\\[1 em]x_3 &= -6.2451\\[1 em]x_4 &= 0.7817+1.9339i\\[1 em]x_5 &= 0.7817-1.9339i \end{aligned} $$Explanation
Polynomial $ x^5+8x^4+12x^3+18x^2+80x+51 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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