If the equation $x^{2} + b^{2} = 1 - 2 b x$ and $x^{2} + a^{2} = 1 - 2 a x$ have one and only one root common, then $| a - b | =$

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Solution

The correct option is C $2$
The equations are ${(x + b)}^{2} = 1$ and ${(x + a)}^{2} = 1$
The solutions for first equation is $x = 1 - b, - 1 - b$
The solutions for second equation is $x = 1 - a, - 1 - a$
For above two equations to have one and only one root common , $1 - b = - 1 - a$
$\Rightarrow a - b = - 2$
$\Rightarrow | a - b | = 2$
The correct option is $C$

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