Q53 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

The sum of the complex roots of the equation $x^4-2 x^3+x-380=0$ is

  • A
    $-3 i+3$
  • B
    $3 \mathrm{i}-3$
  • C
    $-1$
  • Correct answer
    D
    $1$

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... $\begin{aligned} & \therefore \alpha+\beta+5-4=-\frac{(-2)}{1} \\ & \Rightarrow \alpha+\beta+1=2 \\ & \Rightarrow \alpha+\beta=1\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions