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

If x2+px+1 is a factor of 2cos2θx3+2x+sin 2θ, then

A
θ=nπ+π2,nI
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
θ=nπ2,nI
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
θ=nπ,nI
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
θ=2nπ,nI
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C θ=nπ,nI
Let 2cos2θx3+2x+sin 2θ=(x2+px+1)(ax+b)
On expanding the RHS term, and comparing the coefficient of x3 and the constant term with the LHS, we get
a=2cos2θ and b=sin 2θ

2cos2θx3+2x+sin 2θ=(x2+px+1)(2 cos2θx+sin 2θ)
On comparing coefficients of x and x2,
2=p sin 2θ+2 cos2θ2 sin2θ=p sin 2θor p=tanθ ...(i)and 0=sin 2θ+2p cos2θp=tan θ ...(ii)
From Eqs. (i) and (ii),
tanθ=tanθ2 tan θ=0tanθ=0θ=nπ,nI

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