Find roots of polynomial $$ p(x) = x^5+x^4+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.4511\\[1 em]x_2 &= 0.7771+0.6513i\\[1 em]x_3 &= 0.7771-0.6513i\\[1 em]x_4 &= -0.5515+1.0181i\\[1 em]x_5 &= -0.5515-1.0181i \end{aligned} $$Explanation
Polynomial $ x^5+x^4+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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