Find roots of polynomial $$ p(x) = x^5-6x^2+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1656\\[1 em]x_2 &= -0.9377\\[1 em]x_3 &= 1.4865\\[1 em]x_4 &= -0.8572+1.72i\\[1 em]x_5 &= -0.8572-1.72i \end{aligned} $$Explanation
Polynomial $ x^5-6x^2+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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