The integer ' k ', for which the inequality

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 :

  1. (1) 3

  2. (2) 2

  3. (3) 4

  4. (4) 0


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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