wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If α, β are the roots of the quadratic equation ax2+bx+c=0, γ,δ are the roots of px2+qx+r=0 & D1, D2 be the respective discriminants of these equations. If α,β,γ,& δ are in A.P. then D1:D2=
Where α,β,γ,δ,R & a,b,c,p,q,rR)


A

a2:b2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

c2:r2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

a2:r2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

a2:p2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

a2:p2


Given α,β are the roots of the equation ax2+bx+c=0
α+β=ba, αβ=ca

Now, D1=b24ac=a2(b2a24ca)

=a2((α+β)24αβ)

=a2(αβ)2

Also, γ,δ are the roots of the equation px2+qx+r=0

γ+δ=qp, γδ=rp

D2=q24pr=p2(q2p24rp)

=p2(γ+δ)24γδ

=p2(γδ)2

α,β,γ,δ are in A.P

αβ=γδ

D1D2=a2p2

Hence, D1:D2=a2:p2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relations Between Roots and Coefficients
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon