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

If x2+5x+7=0 and ax2+bx+c=0 have a common root and a,b,c N, then the minimum value of a+b+c is .

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
13
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 13
The roots of equation x2+5x+7=0 are non-real. And we know that if a quadratic equation with real coefficients have non real roots, then they occur in conjugate pair.
We are given that the both equations have a common root and a,b,c are natural numbers. It means the roots of the equation ax2 + bx + c = 0have complex roots in conjugate pair. Thus, the both equations have both common roots.
So, a1= b 5=c7=k, kNa=k, b=5k, c=7ka+b+c=13kHence, the minimum value of a+b+c is 13

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Roots under Different Values of Coefficients
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon