Question

Solve the following quadratic equation by factorization :
$a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0$

The roots are $\frac{-1}{a^2},\frac{1}{b^2}$

• A. True
• B. False

Answer 1

The correct option is A True

$a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0$

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

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

$\Rightarrow$ $a^{2}x+1=0$ and $b^{2}x-1=0$

$\Rightarrow$ $a^{2}x=-1$ and $b^{2}x=1$

$\therefore$ $x=\frac{-1}{a^2}$ and $x=\frac{1}{b^2}$

$\therefore$ We can see, roots given in question are correct.