Find roots of polynomial $$ p(x) = x^7+12x+12x+6x+7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2333\\[1 em]x_2 &= -1.4849+0.8832i\\[1 em]x_3 &= -1.4849-0.8832i\\[1 em]x_4 &= 0.0385+1.7657i\\[1 em]x_5 &= 0.0385-1.7657i\\[1 em]x_6 &= 1.563+0.8826i\\[1 em]x_7 &= 1.563-0.8826i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^7+ \color{blue}{12x} + \color{red}{12x} + \color{red}{6x} +7 = x^7+ \color{red}{30x} +7 $$Step 2:
Polynomial $ x^7+30x+7 $ 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