Find roots of polynomial $$ p(x) = x^4+4x^3-4x^2+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4256\\[1 em]x_2 &= -4.8208\\[1 em]x_3 &= 0.6232+0.3147i\\[1 em]x_4 &= 0.6232-0.3147i \end{aligned} $$Explanation
Polynomial $ x^4+4x^3-4x^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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