Find roots of polynomial $$ p(x) = -x^5+4x^4+x^3-15x^2+12x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2533\\[1 em]x_2 &= -1.9295\\[1 em]x_3 &= 3.2888\\[1 em]x_4 &= 1.447+0.6287i\\[1 em]x_5 &= 1.447-0.6287i \end{aligned} $$Explanation
Polynomial $ -x^5+4x^4+x^3-15x^2+12x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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