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

If α,β,γ are the roots of x3x21=0, then the value of 1+α1α+1+β1β+1+γ1γ=


A

6

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

5

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

2

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

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

5


Given equation:
x3x21=0Roots are:α,β,γα+β+γ=1,αβ+βγ+γα=0,αβγ=1.
Now, 1+α1α=2(1α)1α=21α11+α1α=21α1=211α3 (i)Now,1xα+1xβ+1xγ=(xβ)(xγ)+(xα)(xβ)+(xα)(xγ)(xα)(xβ)(xγ)1xα+1xβ+1xγ=3x22xx3x21Let x=111α+11β+11γ=32111=1(i)=211α3=2(1)3=5


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebra of Roots of Quadratic Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon