Find roots of polynomial $$ p(x) = -16384x^7+65536x^6-106496x^5+90120x^4-39680x^3+10752x^2-1344x+63 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.5515\\[1 em]x_2 &= 0.1092+0.0374i\\[1 em]x_3 &= 0.1092-0.0374i\\[1 em]x_4 &= 0.2069+0.3155i\\[1 em]x_5 &= 0.2069-0.3155i\\[1 em]x_6 &= 0.9082+0.6943i\\[1 em]x_7 &= 0.9082-0.6943i \end{aligned} $$Explanation
Polynomial $ -16384x^7+65536x^6-106496x^5+90120x^4-39680x^3+10752x^2-1344x+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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