Find roots of polynomial $$ p(x) = z^4+2z^3-z^3-2z+10 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 1.0626+1.0855i\\[1 em]z_2 &= 1.0626-1.0855i\\[1 em]z_3 &= -1.5626+1.3757i\\[1 em]z_4 &= -1.5626-1.3757i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ z^4+ \color{blue}{2z^3} \color{blue}{-z^3} -2z+10 = z^4+ \color{blue}{z^3} -2z+10 $$Step 2:
Polynomial $ z^4+z^3-2z+10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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