Find roots of polynomial $$ p(x) = x^4-12x^3+75x^2-180x+82 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5858\\[1 em]x_2 &= 3.4142\\[1 em]x_3 &= 4+5i\\[1 em]x_4 &= 4-5i \end{aligned} $$Explanation
Polynomial $ x^4-12x^3+75x^2-180x+82 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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