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

Let α,β,γbe the roots of the equations,x3+ax2+bx+c=0, (a,b,cRand a,b&a,b0). The system of the equations (in u,v,w) given by αu+βv+γw=0;βu+γv+αw=0;γu+αv+βw=0 has non-trivial solutions, then the value of a2b is


A

5

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

1

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

0

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

3

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

The correct option is D

3


Explanation for the correct option:

Finding the value of a2b:

Given that α,β,γbe the roots of the equations,x3+ax2+bx+c=0,

Therefore, α+β+γ=a;αβ+βγ+γα=b

We know that for non-trivial solution

αβγβγαγαβ=0

α3+β3+γ33αβγ=0(α+β+γ)[(α+β+γ)23(αβ+βγ+γα)]=0a(a23b)=0α+β+γ=a;αβ+βγ+γα=b(a23b)=0a2=3ba2b=3

Hence, option (D) is correct.


flag
Suggest Corrections
thumbs-up
16
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon