Question

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

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

Answer 1

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

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 qudratic equation are $-b-\frac{1}{a}$ and $b-\frac{1}{a}$

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