Find roots of polynomial $$ p(x) = 12x^{10}-11x^8-11x^6-12x^4-11 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.3461\\[1 em]x_2 &= 1.3461\\[1 em]x_3 &= 0.7091+0.4843i\\[1 em]x_4 &= 0.7091-0.4843i\\[1 em]x_5 &= -0.7091+0.4843i\\[1 em]x_6 &= -0.7091-0.4843i\\[1 em]x_7 &= -0.3526+0.9167i\\[1 em]x_8 &= -0.3526-0.9167i\\[1 em]x_9 &= 0.3526+0.9167i\\[1 em]x_{10} &= 0.3526-0.9167i \end{aligned} $$Explanation
Polynomial $ 12x^{10}-11x^8-11x^6-12x^4-11 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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