Find roots of polynomial $$ p(x) = 1000x+100x^3+x^5-150 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.1497\\[1 em]x_2 &= -0.0857+3.3598i\\[1 em]x_3 &= -0.0857-3.3598i\\[1 em]x_4 &= 0.0109+9.4197i\\[1 em]x_5 &= 0.0109-9.4197i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1000x+100x^3+x^5-150 & = 0\\[1 em] x^5+100x^3+1000x-150 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^5+100x^3+1000x-150 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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