Find roots of polynomial $$ p(x) = 5x^5+19x^4+x^3+61x^2+48x+12 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -4.2997\\[1 em]x_2 &= -0.3748+0.1982i\\[1 em]x_3 &= -0.3748-0.1982i\\[1 em]x_4 &= 0.6246+1.6477i\\[1 em]x_5 &= 0.6246-1.6477i \end{aligned} $$Explanation
Polynomial $ 5x^5+19x^4+x^3+61x^2+48x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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