The integer k for which the inequality $x^{2} - 2 (4 k - 1) x + 15 k^{2} - 2 k - 7 > 0$ is valid for any x, is

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Solution

The correct option is B
3

$x^{2} - 2 (4 k - 1) x + 15 x^{2} - 2 k - 7 > 0$

$\Rightarrow$ $b^{r} - 4 a c < 0$

$\Rightarrow$ $4 (4 k - 1)^{2}$ -4.1.(15 $k^{2}$ -2k-7)<0

$\Rightarrow$ $k^{2}$ -6k+8<0

$\Rightarrow k ϵ (2, 4)$

$∴$ k=3

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