If f : [ 1 , 2 ] → R defined by f ( x ) = x 2 + 2 k x + k is always negative then the interval in which k lies is

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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

MathematicsQuadratic EquationAP EAMCETAP EAMCET 2017 (26 Apr Shift 2)

Options:

A $\left(\frac{4}{5}, \infty\right)$
B $\left(-\infty,-\frac{4}{5}\right)$
C $\left(-\infty, \frac{4}{5}\right)$
D $\left(-\frac{4}{5}, \infty\right)$

Solution:

1681 Upvotes Verified Answer

The correct answer is: $\left(-\infty,-\frac{4}{5}\right)$

No solution. Refer to answer key.

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