Find roots of polynomial $$ p(x) = 3x^5+10x^3+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6438\\[1 em]x_2 &= 0.3664+0.5741i\\[1 em]x_3 &= 0.3664-0.5741i\\[1 em]x_4 &= -0.0445+1.8295i\\[1 em]x_5 &= -0.0445-1.8295i \end{aligned} $$Explanation
Polynomial $ 3x^5+10x^3+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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