If $x^2+2 p x-2 p+8>0$ for all real values of $x$, then the set of all possible values of $p$ is

If $R-(\alpha, \beta)$ is the range of $\frac{x+3}{(x-1)(x+2)}$, then the sum of the intercepts of the line $\alpha x+\beta y+1=0$ on the coordinate axes is

The roots of the equation $x^4+x^3-4 x^2+x+1=0$ are diminished by $h$ so that, the transformed equation does not contain $x^2$ term. If the values of such $h$ are $\alpha$ and $\beta$, then $12(\alpha-\beta)^2=$

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+a x-c=0$, then