Find roots of polynomial $$ p(x) = 3x^5+19x^3+27x-30 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7658\\[1 em]x_2 &= -0.6609+1.4593i\\[1 em]x_3 &= -0.6609-1.4593i\\[1 em]x_4 &= 0.278+2.2386i\\[1 em]x_5 &= 0.278-2.2386i \end{aligned} $$Explanation
Polynomial $ 3x^5+19x^3+27x-30 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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