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

If a,b,c,d are four consecutive terms of an increasing AP, then the roots of the equation (xa)(xc)+2(xb)(xd)=0 are

A
real and distinct
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
non real complex
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
real and equal
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
integer
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B real and distinct
Since, a,b,c,d are in A.P.
Let a=mn, b=m, c=m+n, d=m+2n,
where, n0
(xa)(xc)+2(xb)(xd)=0
3x2x(a+c+2b+2d)+ac+2bd=0
3x2x(mn+m+n+2m+2m+2n)+(mn)(m+n)+2(m)(m+2n)=0
3x22x(3m+2n)+3m2+4mnn2=0
Now, D=b24ac=4[(3m+2n)23(3m2+4mnn2)]=28n2>0
Therefore, roots are real and distinct.
Ans: A

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equations
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon