The numbers of pairs 
of real numbers, such that whenever 
is a root of the equation 
is also a root of this equation, is:
Text Solution
Verified by ExpertsA
Consider the equation 
If has two roots (not necessarily real 
)
Either 
or 
Case (1) If 
, then it is repeated root. Given that 
is also a root
So, 
or 
When 
then 
then 
Case (2) If 
Then
(I) 
and 
Here 
or 
Hence 
(II) 
and 
Then 
Since 
we get 
Thus 
which implies
Therefore 
(III) 
and 
Thus 
Therefore 
(IV) 
and 
is same as (III)
Therefore we get 6 pairs of (a,b)
Which are 
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