Find roots of polynomial $$ p(x) = x^5-10x^3+12x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.1708\\[1 em]x_2 &= -1.0695\\[1 em]x_3 &= 1.2726\\[1 em]x_4 &= 2.9171\\[1 em]x_5 &= -2.9493 \end{aligned} $$Explanation
Polynomial $ x^5-10x^3+12x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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