1Lets roots be a and b.
a+b=p. ab=q. now both a and b are integers. so p and q are integers.
Now,
p2-4q=0
p2=4q...implies that 4q is always even, so p has to be even....and p2=(2)2(√q)2, so q has to a perfect sq of a positive integer so as to obtain an integral value for p
