Find roots of polynomial $$ p(x) = x^4+x^3+2x^2+4x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.592+1.565i\\[1 em]x_2 &= 0.592-1.565i\\[1 em]x_3 &= -1.092+0.7704i\\[1 em]x_4 &= -1.092-0.7704i \end{aligned} $$Explanation
Polynomial $ x^4+x^3+2x^2+4x+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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