Question

If the inequality $\frac{x^2-kx-2}{x^2-3x+4}>-1$ for every $x\in R$ and S is the sum of all intergral value of K. then find the value of $S^2$

Answer 1

$\frac{x^2-kx-2}{x^2-3x+4}>-1$

$x^2-kx-2>{-x}^2+3x-4$

$f\left(x\right)=2x^2-(k+3)x+2>0$

$f\left(x\right)>0$

$4x-(k+3)>0$

$x>\frac{k+3}{4}$

$k+3<4$

$k<1$

$S^2=0$