The quadratic equations 
and 
have one root in common. The other roots of the first and second equations are integers in the ratio 
. Then, the common root is [JEE Main) 2008]
Text Solution
Verified by Experts2
(2)
Let 
be the common root and other roots be 
and 
respectively.
and 
are roots of 
and 
are roots of 
Now, 
and 
Putting 
in 
, we get 
.
If 
and 
, then 
.
So, roots of the two equations are 2,4 and 2,3 .
Clearly, 2 is the common root.
If 
, then 
.
In this case, roots of the second equation are not integer.
So, 
is not possible.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems