Find roots of polynomial $$ p(x) = 4x^6-45x^5+3491x^2+900 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 5.2858\\[1 em]x_2 &= 10.4928\\[1 em]x_3 &= 0.0004+0.5077i\\[1 em]x_4 &= 0.0004-0.5077i\\[1 em]x_5 &= -2.2647+3.2571i\\[1 em]x_6 &= -2.2647-3.2571i \end{aligned} $$Explanation
Polynomial $ 4x^6-45x^5+3491x^2+900 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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