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

Assertion :Let equations ax2+bx+c=0(a,b,cR) & x2+2x+5=0 have a common root, then a+cb=13. Reason: If both roots of Ax2+Bx+K1=0 & Ax2+Bx+K2=0 are identical, then AA1=BB1=K1K2 (where A,B,K1, and A,B,K2R).

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Assertion is correct but Reason is incorrect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Assertion is incorrect, Reason is correct
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D Assertion is incorrect, Reason is correct
f(x)=x2+2x+5
D=420=16
Hence, it has imaginary roots.
Since it has real coefficients, the roots are conjugates.
Now, a,b,cR.
Since it has a common root with above equation, it too has imaginary roots, occurring in form of conjugates.
Thus, both the equations have equal roots.
Hence, a1=b2=c5=k
Hence, a=k b=2k and c=5k.
Therefore,
a+cb
=6k2k
=3
Hence, assertion is incorrect.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon