Find roots of polynomial $$ p(x) = x^5-5x^4+5x^3-10 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.7029\\[1 em]x_2 &= 1.3075+0.9478i\\[1 em]x_3 &= 1.3075-0.9478i\\[1 em]x_4 &= -0.659+0.7754i\\[1 em]x_5 &= -0.659-0.7754i \end{aligned} $$Explanation
Polynomial $ x^5-5x^4+5x^3-10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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