Question

Which of the following satisfies the equation $a^2{b}^2{x}^2-b^{2}x-a^{2}x+1=0?$

• A. $-\frac{1}{b^2}$
• B. $\frac{1}{b^2}$
• C. $\pm \frac{1}{b^2}$
• D. $-\frac{1}{a^2}$

Answer 1

The correct option is B $\frac{1}{b^2}$

Here, we need to find the roots of the given quadratic equation.

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

$\frac{1}{a^2}$ and $\frac{1}{b^2}$ are the roots of the given quadratic equation and hence, will staisfy the equation.