the condition that roots of px²-px+q=0 are in ratio p:q is

let one be a & other is b then

a= bp/q

a+b = 1

or bp/q +b =1

or b=q/(p+q) .................... (i)     

& ab=q/p

or b²=q²/p²   ....................(ii)                        now equate (i)&(ii)