Question

One of the roots of the equation $(x+\frac{1}{a}{)}^2-b^2=0$ is .

• A. $-ba$
• B. $-a+b$
• C. $-b-\frac{1}{a}$
• D. $b+\frac{1}{a}$

Answer 1

The correct option is C $-b-\frac{1}{a}$

$(x+\frac{1}{a}{)}^2-b^2=0\Rightarrow (x+\frac{1}{a}{)}^2=b^2\Rightarrow (x+\frac{1}{a})=\pm b\Rightarrow x=\pm \left(b\right)-\frac{1}{a}$

Only $-b-\frac{1}{a}$ is listed in the options.

$\Rightarrow -b-\frac{1}{a}$ is one of the roots of the equation.