Find roots of polynomial $$ p(x) = 16x^7+49x^6+6x^5-40x^4+12x^3+6x^2+6x-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5287\\[1 em]x_2 &= -1.5211\\[1 em]x_3 &= -2.4438\\[1 em]x_4 &= 0.5409+0.4i\\[1 em]x_5 &= 0.5409-0.4i\\[1 em]x_6 &= -0.354+0.4754i\\[1 em]x_7 &= -0.354-0.4754i \end{aligned} $$Explanation
Polynomial $ 16x^7+49x^6+6x^5-40x^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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