Find roots of polynomial $$ p(x) = x^6-4x^5+x^4-x^3-5x^2+7x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2458\\[1 em]x_2 &= -1.1233\\[1 em]x_3 &= 1.0569\\[1 em]x_4 &= 3.8611\\[1 em]x_5 &= 0.2255+1.3132i\\[1 em]x_6 &= 0.2255-1.3132i \end{aligned} $$Explanation
Polynomial $ x^6-4x^5+x^4-x^3-5x^2+7x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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