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 x33x2+3x+7=0 and ω is a cube root of unity, then α1β1+β1γ1+γ1α1=

A
ω2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2ω2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3ω2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
3ω2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 3ω2
x33x2+3x+7=0
x33x2+3x1+8=0
(x1)3=8
(x12)3=1
x12=(1)1/3
x12=1,ω,ω2
x=1,12ω,12ω2
α1β1+β1γ1+γ1α1
=22w+2ω2ω2+2ω22
=1ω+1ω+1ω=3ω=3ω2

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Cube Root of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon