Find roots of polynomial $$ p(x) = 3x^5+x^3-5x^2+2x+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8846\\[1 em]x_2 &= 1.03+0.6091i\\[1 em]x_3 &= 1.03-0.6091i\\[1 em]x_4 &= -0.5877+1.3266i\\[1 em]x_5 &= -0.5877-1.3266i \end{aligned} $$Explanation
Polynomial $ 3x^5+x^3-5x^2+2x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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