Find roots of polynomial $$ p(x) = x^4-2x^3+5x^2+x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.1713+0.5819i\\[1 em]x_2 &= -0.1713-0.5819i\\[1 em]x_3 &= 1.1713+2.0156i\\[1 em]x_4 &= 1.1713-2.0156i \end{aligned} $$Explanation
Polynomial $ x^4-2x^3+5x^2+x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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