1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If the equations x2+b2=1−2bx and x2+a2=1−2ax have one and only one common root, then the value of |a−b| is

A
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 2Here a≠b, ∵ For a=b two equations become identical, so they have two roots in common. Let α be the common root of the given equations. Then, α2+b2=1−2bα⋯(1)α2+a2=1−2aα⋯(2) Using equation (1) and (2), b2−a2=2(a−b)α⇒α=−(a+b)2 Putting the value in equation (1), (a+b)24+b2=1+2b×a+b2⇒(a+b)2+4b2=4+4b2+4ab⇒(a+b)2−4ab=4⇒(a−b)2=4∴|a−b|=2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Quadratic Equations with Exactly One Root Common
MATHEMATICS
Watch in App
Join BYJU'S Learning Program