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:
$D<0$
$(2(3 k-1))^{2}-4\left(8 k^{2}-7\right)<0$
$4\left(9 k^{2}-6 k+1\right)-4\left(8 k^{2}-7\right)<0$
$k^{2}-6 k+8<0$
$(k-4)(k-2)<0$
$2 then $k=3$
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