Question

Solve the following quadratic equation by factorization :
$x^2+(a+\frac{1}{a})x+1=0$

the roots are $-a,-\frac{1}{a}$

• A. True
• B. False

Answer 1

The correct option is A True

$x^2+(a+\frac{1}{a})x+1=0$

$\Rightarrow$ $x^2+ax+\frac{x}{a}+1=0$

$\Rightarrow$ $x(x+a)+\frac{1}{a}(x+a)=0$

$\Rightarrow$ $(x+a)(x+\frac{1}{a})=0$

$\Rightarrow$ $x+a=0$ and $x+\frac{1}{a}=0$

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

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