Find roots of polynomial $$ p(x) = x^5-4x-4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.597\\[1 em]x_2 &= -1.0022+0.3241i\\[1 em]x_3 &= -1.0022-0.3241i\\[1 em]x_4 &= 0.2037+1.4886i\\[1 em]x_5 &= 0.2037-1.4886i \end{aligned} $$Explanation
Polynomial $ x^5-4x-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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