Question

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

• A. $2$
• B. $3$
• C. $4$
• D. None of these

Answer 1

The correct option is B $3$

The inequality will be greater than zero

if D is less than zero.

$D<0$

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

Simplifying this we get

$K^2-6k+8<0$

$(k-4)(k-2)<0$

$\therefore k$ lies in $(2,4)$

In this interval only one integer is present i.e $3$

$\therefore k=3$