For what values of $k$ is the inequality $x^2-(k-3)x-k+6>0$ valid for all real $x$?

Q. Find all values of $k$ for which the inequality , $2x^2-4k^{2}x-k^2+1>0$ is valid for all real $x$ which do not exceed unity in the absolute value.

Q. For what integral $k$ is the inequality $x^2-2(4k-1)x+15k^2-2k-7>0$ valid for any real $x$?

Q. The integer $k$ for which the inequality $x^2-2(4k-1)x+15k^2-2k-7>0$ is valid for $x$, is

Q.

The integer k for which the inequality

x²−2(4k−1)x+15k²-2k−7>0 is valid for any x, is?

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