If $f:[1,2] \rightarrow \mathbb{R}$ defined by $f(x)=x^2+2 k x+k$ is always negative then the interval in which $k$ lies is

• A

  $\left(\frac{4}{5}, \infty\right)$
• Correct answer
  B

  $\left(-\infty,-\frac{4}{5}\right)$
• C

  $\left(-\infty, \frac{4}{5}\right)$
• D

  $\left(-\frac{4}{5}, \infty\right)$

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