The sum of the complex roots of the equation $x^4-2 x^3+x-380=0$ is
The sum of the complex roots of the equation $x^4-2 x^3+x-380=0$ is
$-3 i+3$
$3 \mathrm{i}-3$
$-1$
$1$
Solution
$x^4-2 x^3+x-380=0$
$\begin{aligned} & \text { put } x=5 \\ & 5^4-2 \times 5^3+5-380=\Rightarrow 0=0\end{aligned}$
So, $x=5$ one real root
put $\mathrm{n}=-4$
$(-4)^4-2 x(-4)^3+(-4)-380=0 \Rightarrow 0=0$
So, $n=-4$ is second real roots.
Let $\alpha$ and $\beta$ are two other roots...
$\begin{aligned} & \therefore \alpha+\beta+5-4=-\frac{(-2)}{1} \\ & \Rightarrow \alpha+\beta+1=2 \\ & \Rightarrow \alpha+\beta=1\end{aligned}$