Find roots of polynomial $$ p(x) = 3x^9+2x^5+9x^7+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8639\\[1 em]x_2 &= 0.7938+0.3844i\\[1 em]x_3 &= 0.7938-0.3844i\\[1 em]x_4 &= -0.5877+0.7279i\\[1 em]x_5 &= -0.5877-0.7279i\\[1 em]x_6 &= 0.2415+0.9836i\\[1 em]x_7 &= 0.2415-0.9836i\\[1 em]x_8 &= -0.0157+1.662i\\[1 em]x_9 &= -0.0157-1.662i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 3x^9+2x^5+9x^7+5 & = 0\\[1 em] 3x^9+9x^7+2x^5+5 & = 0 \end{aligned} $$Step 2:
Polynomial $ 3x^9+9x^7+2x^5+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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