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

If a,b,c are distinct rational numbers, then the roots of the quadratic equation (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0 are

A
imaginary
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
irrational
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
rational and distinct
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
rational and equal
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C rational and distinct
(a+b2c)x2+(b+c2a)x+(c+a2b)=0
Sum of coefficients =0
Since, the sum of coefficients is zero, so the given quadratic equation has one root to be 1.

Let another root be α.
Product of roots =c+a2ba+b2c
1×α=a+c2ba+b2c
α=a+c2ba+b2c
Roots are rational and distinct.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon