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

The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x211x+α=0 are rational numbers is :

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 3
6x211x+α=0
If roots are rational numbers, then discriminant should be a perfect square.
D=12124α
So, If α=1, D=97, which is not a perfect square.
α=2, D=73, which is not a perfect square.
α=3, D=49, it is a perfect square.
α=4, D=25, it is a perfect square.
α=5, D=1, it is a perfect square.

So, number of possible values of α is 3.

flag
Suggest Corrections
thumbs-up
73
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Nature and Location of Roots
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon