the answer is option d)
see
( aq - bp ) ( br - cq )=abqr-acq²-b²pr+bpcq
then sum of roots for first equation
α+β=-b/a,αβ=c/a
and second is
α+ω=-q/p,αω=r/p
so
-b/a-β=-q/p-ω
ω=b/a-q/p+β
as
c/(aβ)=r/(pω)
ω=raβ/cp=b/a-q/p+β
therefore β=(b/a-q/p)/((ra/cp)-1)
[tex] \beta = \frac{(pb-aq)}{ap} \frac{(ra-cp)}{cp} [/tex]
and
ω=(ra/cp)((b/a-q/p)/((ra/cp)-1))
[tex]= \frac{ra}{cp} \frac{(pb-aq)}{ap} \frac{(ra-cp)}{cp}[/tex]
