Find roots of polynomial $$ p(x) = 7x^6+6x^5+5x^4+4x^3+3x^2+2x-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2933\\[1 em]x_2 &= -0.8866\\[1 em]x_3 &= -0.4791+0.7327i\\[1 em]x_4 &= -0.4791-0.7327i\\[1 em]x_5 &= 0.3472+0.7722i\\[1 em]x_6 &= 0.3472-0.7722i \end{aligned} $$Explanation
Polynomial $ 7x^6+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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