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

If both the roots of the quadratic equation x22kx+k2+k5=0 are less than 5, then k lies in the interval

A
(5, 6]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(6,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(,4)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
[4,5]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C (,4)
f(x)=x22kx+k2+k5
both roots are less than 5, then
(i) Discriminant 0
(ii)f(5)>0(iii)Sum of roots2<5
Hencei) (4k24(k2+k5)04k24k24k+2004k20k5

(ii) f(5)>0;2510k+k2+k5>0or k29k+20>0or k(k4)5(k4)>0or(k5)(k4)>0kϵ(,4)(5,)(iii) Sum of roots2=b2a=2k2<5
The intersection of (i), (ii) & (iii) gives k ϵ(,4).

flag
Suggest Corrections
thumbs-up
0
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