1. What is the set of values for p for which p(x2+2)<2x2+6x+1 for all real values of x?

note that for the above inequality to be true for all real x , both and

2. Find the set of values for k for which x2+3kx+k is positive for all real values of x.

both inequalities must hold ...3. Find the set of values of x for which x2+x+1<x+2<x2-6x+12

and

take the intersection of the solution sets