Number of real values of p for which the equations x2−px+8=0 and x2+p=0 have two integral solutions is

Let α and β be two integral solutions of x2−px+8=0 α+β=p and αβ=8 Since α and β are integers, hence (α,β) can be (8,1),(4,2) , (−8,−1) and (−4,−2) and possible values of p can be 9,6,−9,−6 but only for p=−9,x2+p=0 will have two integral solutions.  Hence only one value of p . i.e. p=−9 .