Find roots of polynomial $$ p(x) = 16x^7+49x^6+6x^5+35x^4+12x^3+6x^2+6x-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.3892\\[1 em]x_2 &= -0.6744\\[1 em]x_3 &= -3.1428\\[1 em]x_4 &= -0.1713+0.7277i\\[1 em]x_5 &= -0.1713-0.7277i\\[1 em]x_6 &= 0.3541+0.7433i\\[1 em]x_7 &= 0.3541-0.7433i \end{aligned} $$Explanation
Polynomial $ 16x^7+49x^6+6x^5+35x^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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