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

If α,β,γ are the roots of x3+ax2+bx+c=0, then (α+β2γ)=

A
2a39ab+27c
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2a3+9ab+27c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2a39ao27c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2a3+9ao27c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 2a39ab+27c
As α,β,γ are roots of x3+ax2+bx+c=0
Gives
s1=α+β+γ=aα+β=aγs2=αβ+βγ+γα=bs3=αβγ=c
Therefore,
Π(α+β2γ)=Π(a2γ)=(a+3α)(a+3β)(a+3γ)=(a3+3a2(α+β+γ)+3a(αβ+βγ+γα)+2+αβγ)=(a33a3+9ab27c)=2a39ab+27c

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