Find roots of polynomial $$ p(x) = x^7+x^5+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8899\\[1 em]x_2 &= 0.7861+0.4633i\\[1 em]x_3 &= 0.7861-0.4633i\\[1 em]x_4 &= -0.5+0.866i\\[1 em]x_5 &= -0.5-0.866i\\[1 em]x_6 &= 0.1589+1.1509i\\[1 em]x_7 &= 0.1589-1.1509i \end{aligned} $$Explanation
Polynomial $ x^7+x^5+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
This page was created using
Polynomial Roots Calculator