Question

Solve the following quadratic equation by factorization :
$a(x^2+1)-x(a^2+1)=0$

• A. $-a$, $\frac{1}{a}$
• B. $a$, $\frac{1}{a}$
• C. $a$, $\frac{-1}{a}$
• D. $-a$, $\frac{-1}{a}$

Answer 1

Answer: (B)

$a$, $\frac{1}{a}$

$a(x^2+1)-x(a^2+1)=0$

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

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

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

$\Rightarrow$ $ax(x-a)-1(x-a)=0$

$\Rightarrow$ $(x-a)(ax-1)=0$

$\Rightarrow$ $x-a=0$ and $ax-1=0$

$\Rightarrow$ $x=a$ and $x=\frac{1}{a}$