CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The condition that the product of two roots of ax3+bx2+cx+d=0 may be equal to 1, is:

A
c(a+d)+b(a+d)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
d(b+d)+a(a+c)=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
a(b+c)+b(c+d)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a(a+b)+d(a+c)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B d(b+d)+a(a+c)=0
Let α,β,γ are the roots of ax3+bx2+cx+d=0
Such that αβ=1
S1=α+β+γ=baα+β=baγS2=αβ+βγ+γα=caγ(α+β)=ca+1=c+aaS3=αβγ=daγ=da
From S1 and S3,
α+β=bada=(b+d)a (4)
From S2 and (4), we have
(b+d)a(da)=c+aad(b+d)+a(a+c)=0
Hence, option 'B' is correct.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q9
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon