Find roots of polynomial $$ p(x) = x^4-4x^3+8x^2-8x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1+i\\[1 em]x_2 &= 1-i\\[1 em]x_3 &= 1+i\\[1 em]x_4 &= 1-i \end{aligned} $$Explanation
Polynomial $ x^4-4x^3+8x^2-8x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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