Question:
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 :
Correct Option: 1
Solution:
$x^{2}-2(3 K-1) x+8 K^{2}-7>0$
Now, $D<0$
$\Rightarrow 4(3 K-1)^{2}-4 \times 1 \times\left(8 K^{2}-7\right)<0$
$\Rightarrow 9 K^{2}-6 K+1-8 K^{2}+7<0$
$\Rightarrow K^{2}-6 K+8<0$
$\Rightarrow(K-4)(K-2)<0$
$\Rightarrow \quad \mathrm{K} \in(2,4)$
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