Find roots of polynomial $$ p(x) = x^5+3x^4+5x^3-4x^2+x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6203\\[1 em]x_2 &= 0.6013+0.5606i\\[1 em]x_3 &= 0.6013-0.5606i\\[1 em]x_4 &= -1.7912+1.987i\\[1 em]x_5 &= -1.7912-1.987i \end{aligned} $$Explanation
Polynomial $ x^5+3x^4+5x^3-4x^2+x+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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