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 Ab2=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 1−m+1−m+b=1m+1m+b⇒2m=1b−m−1b+m⇒2m=2mb2−m2⇒m2=b2−m2⇒b2=2m2