Find roots of polynomial $$ p(x) = 21x^6+48x^3-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2743\\[1 em]x_2 &= -1.3212\\[1 em]x_3 &= -0.1372+0.2376i\\[1 em]x_4 &= -0.1372-0.2376i\\[1 em]x_5 &= 0.6606+1.1442i\\[1 em]x_6 &= 0.6606-1.1442i \end{aligned} $$Explanation
Polynomial $ 21x^6+48x^3-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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