Question

As raízes complexas do polinômio T(x) = x³ + 2x² + x + 2 são:

Answer 1

$T(x)=x^3+2x^2+x+2\\\\\\0=x^3+2x^2+x+2\longrightarrow0=x^3+x+2x^2+2\longrightarrow\\\\0=x(x^2+1)+2(x^2+1)\longrightarrow0=(x+2)(x^2+1)\left\langle\begin{array}{lcl}0=x+2\\\\0=x^2+1\end{array}\right\\\\\begin{matrix}x=-2\end{matrix}\qquad\text{ou}\qquad\begin{matrix}x=\pm{i}\end{matrix}\\\\\\\boxed{S=\{-2{,}\ \pm{i}\}}$

As raízes complexas são $-i$ e $+i$.