Find roots of polynomial $$ p(x) = z^4+z^3+5z^2+7 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 0.2973+1.2358i\\[1 em]z_2 &= 0.2973-1.2358i\\[1 em]z_3 &= -0.7973+1.9227i\\[1 em]z_4 &= -0.7973-1.9227i \end{aligned} $$Explanation
Polynomial $ z^4+z^3+5z^2+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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