Which of the following is a root of the quadratic equation $(x + \frac{1}{a})^{2} - b^{2} = 0$ ?

\frac{- b}{a}

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- b - \frac{1}{a}

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- a b

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b + \frac{1}{a}

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Solution

The correct option is B $- b - \frac{1}{a}$
Given quadratic equation is $(x + \frac{1}{a})^{2} - b^{2} = 0 \Rightarrow (x + \frac{1}{a})^{2} = b^{2} \Rightarrow (x + \frac{1}{a}) = \pm b \Rightarrow x = \pm b - \frac{1}{a}$

$\Rightarrow$ Roots of the quadratic equation are $- b - \frac{1}{a}$ and $b - \frac{1}{a}$

$∴$ Among the given options, one root of the quadratic equation is $- b - \frac{1}{a}$ .

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