Find roots of polynomial $$ p(x) = 3x^5-8x^4+2x^3+5x^2-2x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8291\\[1 em]x_2 &= 1.2233\\[1 em]x_3 &= 1.9571\\[1 em]x_4 &= 0.1577+0.3783i\\[1 em]x_5 &= 0.1577-0.3783i \end{aligned} $$Explanation
Polynomial $ 3x^5-8x^4+2x^3+5x^2-2x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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