Find roots of polynomial $$ p(x) = 3x^6-6x^5-2x^4+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1274\\[1 em]x_2 &= 2.2501\\[1 em]x_3 &= 0.1743+0.9944i\\[1 em]x_4 &= 0.1743-0.9944i\\[1 em]x_5 &= -0.863+0.5354i\\[1 em]x_6 &= -0.863-0.5354i \end{aligned} $$Explanation
Polynomial $ 3x^6-6x^5-2x^4+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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