wiz-icon
MyQuestionIcon
MyQuestionIcon
17
You visited us 17 times! Enjoying our articles? Unlock Full Access!
Question

If both the roots of the quadratic equation ax2+bx+c=0 are negative, then

A
a,b,c can be any negative integers
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a,b,c can be any positive rational numbers
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
a,b,c can be any real numbers
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a,b,c can be any integers
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct options are
A a,b,c can be any negative integers
B a,b,c can be any positive rational numbers
As both the roots are negative, so
α+β<0ba<0ba>0(1)α×β>0ca>0(2)

When a>0, using equation (1) and (2), we get
b>0, c>0
Similarly, when a<0, using equation (1) and (2), we get
b<0, c<0

Hence, a,b,c has to be of same sign.

flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon