The values of p for which one root of the equation x2−(p + 1) x+p2+p=8 exceeds 2 and the other is lesser than 2 are given by

Let f(x)=x2−(p+1)x+p2+p−8Since one root is less than 2 and other is more than 2, 2lies between the roots⇒    f(2)<0⇒    4−2(p+1)+p2+p−8<0⇒    p2−p−6<0⇒    (p−3)(p+2)<0⇒    p∈(−2,3)