Find roots of polynomial $$ p(x) = 15x^4+30x^6+5x-20 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.82\\[1 em]x_2 &= -0.8909\\[1 em]x_3 &= -0.394+0.919i\\[1 em]x_4 &= -0.394-0.919i\\[1 em]x_5 &= 0.4295+0.8534i\\[1 em]x_6 &= 0.4295-0.8534i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 15x^4+30x^6+5x-20 & = 0\\[1 em] 30x^6+15x^4+5x-20 & = 0 \end{aligned} $$Step 2:
Polynomial $ 30x^6+15x^4+5x-20 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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