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:

Question

The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 &#62; 0 is valid for every x in R is:

Aicharya · Accepted Answer

x 2 - 2 3 k - 1 x + 8 k 2 - 7 &#62; 0 Now, D &#60; 0 &#8658; &#160; 4 3 k - 1 2 - 4 &#215; 1 &#215; 8 k 2 - 7 &#60; 0 &#8658; &#160; 9 k 2 - 6 k + 1 - 8 k 2 + 7 &#60; 0 &#8658; &#160; k 2 - 6 k + 8 &#60; 0 &#8658; &#160; k - 4 k - 2 &#60; 0 &#8658; &#160; k &#8712; 2 , 4 &#8658; k = 3

The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 &#62; 0 is valid for every x in R is:

Solution

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: