Find roots of polynomial $$ p(x) = 1+2z^4 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 0.5946+0.5946i\\[1 em]z_2 &= 0.5946-0.5946i\\[1 em]z_3 &= -0.5946+0.5946i\\[1 em]z_4 &= -0.5946-0.5946i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1+2z^4 & = 0\\[1 em] 2z^4+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ 2z^4+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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