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Question

The condition that the equation 1x+1x+b=1m+1m+b has real roots, that are equal in magnitude but opposite in sign, is

A
b2=2m2
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B
b2=m2
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C
2b2=m2
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D
b2=4m2
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Solution

The correct option is A b2=2m2
Clearly, x=m is a root of the equation.
Therefore, the other root must be m.
Putting the value of x=m in the given equation, we get
1m+1m+b=1m+1m+b2m=1bm1b+m2m=2mb2m2m2=b2m2b2=2m2

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