Find roots of polynomial $$ p(x) = -16384x^7+61446x^6-94208x^5+39936x^4-7424x^3+512x^2-320x+63 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.1934\\[1 em]x_2 &= -0.1082+0.1699i\\[1 em]x_3 &= -0.1082-0.1699i\\[1 em]x_4 &= 0.2751+0.2207i\\[1 em]x_5 &= 0.2751-0.2207i\\[1 em]x_6 &= 1.6116+1.1589i\\[1 em]x_7 &= 1.6116-1.1589i \end{aligned} $$Explanation
Polynomial $ -16384x^7+61446x^6-94208x^5+39936x^4-7424x^3+512x^2-320x+63 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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