Find roots of polynomial $$ p(x) = 16x^7+49x^6+6000x^5+25x^4+12x^3+6x^2+6x-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2213\\[1 em]x_2 &= 0.0883+0.2264i\\[1 em]x_3 &= 0.0883-0.2264i\\[1 em]x_4 &= -0.201+0.153i\\[1 em]x_5 &= -0.201-0.153i\\[1 em]x_6 &= -1.5292+19.3041i\\[1 em]x_7 &= -1.5292-19.3041i \end{aligned} $$Explanation
Polynomial $ 16x^7+49x^6+6000x^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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