Find roots of polynomial $$ p(x) = 1-x^2+x^4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.866+0.5i\\[1 em]x_2 &= 0.866-0.5i\\[1 em]x_3 &= -0.866+0.5i\\[1 em]x_4 &= -0.866-0.5i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1-x^2+x^4 & = 0\\[1 em] x^4-x^2+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^4-x^2+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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