Find roots of polynomial $$ p(x) = 16x^7-35x^6+6x^5+25x^4+12x^3+6x^2+6x-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4128\\[1 em]x_2 &= 0.0077+0.6619i\\[1 em]x_3 &= 0.0077-0.6619i\\[1 em]x_4 &= -0.6902+0.3396i\\[1 em]x_5 &= -0.6902-0.3396i\\[1 em]x_6 &= 1.5699+0.6748i\\[1 em]x_7 &= 1.5699-0.6748i \end{aligned} $$Explanation
Polynomial $ 16x^7-35x^6+6x^5+25x^4+12x^3+6x^2+6x-5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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