Find roots of polynomial $$ p(x) = 1-2x^7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9057\\[1 em]x_2 &= 0.5647+0.7081i\\[1 em]x_3 &= 0.5647-0.7081i\\[1 em]x_4 &= -0.2015+0.883i\\[1 em]x_5 &= -0.2015-0.883i\\[1 em]x_6 &= -0.816+0.393i\\[1 em]x_7 &= -0.816-0.393i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1-2x^7 & = 0\\[1 em] -2x^7+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ -2x^7+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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