Find roots of polynomial $$ p(x) = 5x^4+12x^3+6x^2+2x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2365+0.6522i\\[1 em]x_2 &= 0.2365-0.6522i\\[1 em]x_3 &= -1.4365+0.1189i\\[1 em]x_4 &= -1.4365-0.1189i \end{aligned} $$Explanation
Polynomial $ 5x^4+12x^3+6x^2+2x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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