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

If b2>4ac, then a(x2+4x+4)2+b(x2+4x+4)+c=0 has distinct real roots if ?

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

The correct option is C b < 0 < a < c
Let x2+4x+4=y, then the equation becomes ay2+by+c=0 ...(1)
b24ac>0 equation (1) has two distinct real roots, say α and β
y=α or βx2+4x+4=α or β
(x+2)2=α or β ...(2)
Clearly equation (2) will give four distinct real values of x if α and β are positive. That is if equation (1) has positive roots. For this a and c should have the same sign and the sign of b should be negative. Only the option (c) satisfies this condition.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Quadratic Equations
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon