Find roots of polynomial $$ p(x) = -49x^2+5x^8+54 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1758+0.1206i\\[1 em]x_2 &= 1.1758-0.1206i\\[1 em]x_3 &= -1.1758+0.1206i\\[1 em]x_4 &= -1.1758-0.1206i\\[1 em]x_5 &= -0.7016+1.3639i\\[1 em]x_6 &= -0.7016-1.3639i\\[1 em]x_7 &= 0.7016+1.3639i\\[1 em]x_8 &= 0.7016-1.3639i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} -49x^2+5x^8+54 & = 0\\[1 em] 5x^8-49x^2+54 & = 0 \end{aligned} $$Step 2:
Polynomial $ 5x^8-49x^2+54 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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