The integer ' k ', for which the inequality


The integer ' $k$ ', for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R$, is :

  1. 3

  2. 2

  3. 0

  4. 4

Correct Option: 1


$x^{2}-2(3 K-1) x+8 K^{2}-7>0$

Now, $D<0$

$\Rightarrow 4(3 K-1)^{2}-4 \times 1 \times\left(8 K^{2}-7\right)<0$

$\Rightarrow 9 K^{2}-6 K+1-8 K^{2}+7<0$

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


$\Rightarrow \quad \mathrm{K} \in(2,4)$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now