Find roots of polynomial $$ p(x) = 4x^{10}-9x^3+24x-18 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9695\\[1 em]x_2 &= -1.2266\\[1 em]x_3 &= 0.8583+0.405i\\[1 em]x_4 &= 0.8583-0.405i\\[1 em]x_5 &= -1.039+0.7549i\\[1 em]x_6 &= -1.039-0.7549i\\[1 em]x_7 &= -0.2927+1.2776i\\[1 em]x_8 &= -0.2927-1.2776i\\[1 em]x_9 &= 0.602+1.0586i\\[1 em]x_{10} &= 0.602-1.0586i \end{aligned} $$Explanation
Polynomial $ 4x^{10}-9x^3+24x-18 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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