Find roots of polynomial $$ p(x) = 12x^5+6x^3-5x-8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9204\\[1 em]x_2 &= -0.6318+0.4792i\\[1 em]x_3 &= -0.6318-0.4792i\\[1 em]x_4 &= 0.1716+1.0595i\\[1 em]x_5 &= 0.1716-1.0595i \end{aligned} $$Explanation
Polynomial $ 12x^5+6x^3-5x-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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