Let x1 , x2 be the roots of the equation x2−3x+p=0 and let  x3, x4 be the roots of the equation x2−12x+q=0 .If the number x1 ,x2 ,x3 ,x4 (in order) form an increasing G.P., then

It is given that  x1 , x2 are roots of x2−3x+p=0⇒x1+x2=3 , x1x2=px3, x4 are roots of x2−12x+q=0 ⇒x3+x4=12 and x3 x4=qIt is given that x1 , x2 , x3 ,x4 form an increasing G.P. Therefore, x1=a,x2=ar,x3=ar2,x4=ar3, where r>1Now , x1+x2=3⇒a(1+r)=3x3+x4=12⇒ar2(1+r)=12⇒r=2 and a=1∴ x1=1,x2=2,x3=4,x4=8Thus , p=x1x2=2 and  q=x3x4=32.