Question

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

• A. 3
• B. 2
• C. 0
• D. 4

Answer 1

Answer: (A)

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