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

∣ ∣x+1x+2x+λx+2x+3x+μx+3x+4x+ν∣ ∣=0, where λ,μ,ν are in A.P. is

A
an equation whose all roots are real
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
an identity in x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
an equation with only one real root
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C an identity in x
Given, λ,μ,ν are in A.P.
2μ=λ+ν
Now, ∣ ∣x+1x+2x+λx+2x+3x+μx+3x+4x+ν∣ ∣=0
R1R1+R3
∣ ∣ ∣2(x+2)2(x+3)2x+2μx+2x+3x+μx+3x+4x+ν∣ ∣ ∣=0
2∣ ∣x+2x+3x+μx+2x+3x+μx+3x+4x+ν∣ ∣=0
Since, R1,R2 are identical . So the determinant is 0.
Thus, we can say that the determinant value is 0 irrespective of value of x . That means for all values of x.
Hence, it is an identity in x.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon