Find roots of polynomial $$ p(x) = 2x^4+x^3+x^2+x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.371+0.8038i\\[1 em]x_2 &= 0.371-0.8038i\\[1 em]x_3 &= -0.621+0.5023i\\[1 em]x_4 &= -0.621-0.5023i \end{aligned} $$Explanation
Polynomial $ 2x^4+x^3+x^2+x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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