Find roots of polynomial $$ p(x) = x^5-5x^4+x^3-x^2-x+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.0328\\[1 em]x_2 &= 1.1648\\[1 em]x_3 &= 4.83\\[1 em]x_4 &= 0.019+1.1732i\\[1 em]x_5 &= 0.019-1.1732i \end{aligned} $$Explanation
Polynomial $ x^5-5x^4+x^3-x^2-x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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