Find roots of polynomial $$ p(x) = -x^4+x^3-x^2-x-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4334+0.5258i\\[1 em]x_2 &= -0.4334-0.5258i\\[1 em]x_3 &= 0.9334+1.1325i\\[1 em]x_4 &= 0.9334-1.1325i \end{aligned} $$Explanation
Polynomial $ -x^4+x^3-x^2-x-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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