Question

The roots of the equation $ a({{x}^{2}}+1)-({{a}^{2}}+1)x=0 $ are:

• A. $ a,\frac{1}{a} $
• B. $ a,2a $
• C. $ a,\frac{1}{2a} $
• D. none of these

Answer 1

Answer: (A)

We have
$a\left(x^{2}+1\right)-\left(a^{2}+1\right) x=0$
$\Rightarrow a x^{2}-\left(a^{2}+1\right) x+a=0$
$\Rightarrow \left(a x^{2}-a^{2} x\right)-(x-a)=0$
$\Rightarrow a x(x-a)-1(x-a)=0$
$\Rightarrow (x-a)(a x-1)=0$
$\Rightarrow x=a, \frac{1}{a}$