Find roots of polynomial $$ p(x) = x^5+x^4-x^3+11x^2+8x-28 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1942\\[1 em]x_2 &= -2.0731+0.4305i\\[1 em]x_3 &= -2.0731-0.4305i\\[1 em]x_4 &= 0.976+2.0683i\\[1 em]x_5 &= 0.976-2.0683i \end{aligned} $$Explanation
Polynomial $ x^5+x^4-x^3+11x^2+8x-28 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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