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

If both the roots α,β of the quadratic equation ax2+bx+c=0,a<0 are less than a real number k such that k>α>β
Considering f(x)=ax2+bx+c, select the correct statement(s).

A
f(k)<0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
k<b2a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
D>0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
f(k)>0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C D>0
Given the quadratic polynomial: f(x)=ax2+bx+c,a<0
Let α,β be it's roots of f(x)=0.
Now, k is a real number such that k>α>β
So, we can draw the graph as:


Clearly, for this to happen, the following conditions needs to be satisfied:
(a) D>0 because f(x)=0 has 2 distinct roots.
(b) f(k)<0.
(c) Abscissa of Vertex =b2a<k

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Location of Roots when Compared with a constant 'k'
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon