Find roots of polynomial $$ p(x) = x^4+x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7271+0.9341i\\[1 em]x_2 &= 0.7271-0.9341i\\[1 em]x_3 &= -0.7271+0.43i\\[1 em]x_4 &= -0.7271-0.43i \end{aligned} $$Explanation
Polynomial $ x^4+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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