Question

Qu
24. a?b?x2 + b²x - a²x – 1= 0

this is a quadratic equations​

Answer 1

Hey There!!

Here your quadratic equation is:

a^2b^2x^2+b^2x-a^2x-1=0a

2

b

2

x

2

+b

2

x−a

2

x−1=0

Here, this equation can be factorised.

Take out b^2xb

2

x common first and second term.

Also take -1−1 common from third and fourth term.

$$\begin{lgathered}a^2b^2x^2+b^2x-a^2x-1=0 \\ \\ \implies b^2x(a^2x+1)-1(a^2x+1) = 0 \\ \\ \implies (a^2x+1)(b^2x-1)=0\\ \\ \implies a^2x+1=0 \,\, or \, \, b^2x-1=0 \\ \\ \implies \boxed{x=-\frac{1}{a^2}} \, \, or \, \, \boxed{x=\frac{1}{b^2}}\end{lgathered}$$

Hope it helps