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 :

• A. 3
• B. 2
• C. 0
• D. 4

Answer 1

Answer: (A)

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