Question

the ratio of roots of equation ax2 + bx + c =0 and px2 +qx +r = 0 are equal .if D1 and D2 are respective descrimants ,then what is D1/D2 equal to​

Answer 1

Answer: Let α1,β1 are roots of ax2+bx+c=0 and

α2,β2 are roots of px2+qx+r=0

Given:α1β1=α2β2 and D1=b2−4ac,D2=q2−4pr

Also we know that

α1+β1=−ba, α1β1=ca

α2+β2=−qp, α2β2=rp

Using componendo and dividendo we get

α1+β1α1−β1=α2+β2α2−β2

⇒(α1+β1)2(α1−β1)2=(α2+β2)2(α2−β2)2

⇒b2a2b2a2−4ca=q2p2q2p2−4rp

⇒b2b2−4ac=q2q2−4pr

⇒b2D1=q2D2

⇒D1:D2=b2:q2