The integer k, for which the inequality x ^ 2 - 2(3k - 1)x + 8 k ^...

Now, $D < 0$

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

$⇒ 9{k}^{2} - 6k + 1 - 8{k}^{2} + 7 < 0$

$⇒ {k}^{2} - 6k + 8 < 0$

$⇒ \left(k - 4\right)\left(k - 2\right) < 0$

$⇒ k \in \left(2, 4\right)$

$⇒ k = 3$