Question

Solve the following quadratic equation by factorization method: [2 MARKS]

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

Answer 1

Concept :1 Mark
Application : 1 Mark

(i) We have,

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

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

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

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

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

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

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