Find roots of polynomial $$ p(x) = 6x^5+5x^4+4x^3+3x^2+2x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6703\\[1 em]x_2 &= 0.2942+0.6684i\\[1 em]x_3 &= 0.2942-0.6684i\\[1 em]x_4 &= -0.3757+0.5702i\\[1 em]x_5 &= -0.3757-0.5702i \end{aligned} $$Explanation
Polynomial $ 6x^5+5x^4+4x^3+3x^2+2x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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