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

All the values of a for which the quadratic expression ax2+(a2)x2 is negative for exactly two integral values of x may lie in

A
[1,3/2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[3/2,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[1,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
[1,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C [1,2)
ax2+(a2)x2

The discriminant =(a2)24(a)(2)

=a24a+4+8a

=a2+4a+4

=(a+2)2

That's the positive for all a, so there are always two roots.

Now if a>0, then the quadratic is negative between those two real roots.
Using quadratic formula for roots:
2a(a+2)2a<x<2a+a+22a

1<x<2a

For it exactly 2 integer values of x are in that interval, the integer must be 0 and +1.

That requires 1<2a2.

Taking reciprocals:

1>a212 [ In equality direction is reversed by reciprocal ]

2>a1 [ Multiply by 2 ]

a[1,2)



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