and 
are integers. If the A.M. of the roots of 
and G.M. of the roots of 
are equal, then
is an odd integer
is an even integer 
is an even integer
is an odd integer
Text Solution
Verified by ExpertsC
Analyze the First Equation
For the quadratic equation 
, let its roots be 
and 
.
Sum of roots: 
Arithmetic Mean (A.M.) of the roots:
Analyze the Second Equation
For the quadratic equation 
, let its roots be 
and 
.
Product of roots: 
Geometric Mean (G.M.) of the roots:
Set Them Equal
According to the problem, the A.M. of the first equation equals the G.M. of the second:
Conclusion
Since 
is given to be an integer, 
is also an integer. Multiplying any integer by 2 always results in an even integer. Therefore, 
must be an even integer.
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