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

If the equation ax2+bx+c=0 has non-real roots,prove that 1+ca+ba>0

Open in App
Solution

The equation ax2+bx+c=0 is non-real
b24ac<0
b2<4ac
|b|<2ac
b<a+c
a+cb>0
a+b+c>0
As A.M> G.M
a+c2>ac
a+c>2ac
a+c2>ac
b<ac
a+b+c>0
aa+ba+ca>0 by dividing by a
1+ba+ca>0
Hence proved


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