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

Given:

Given quadratic equation is $x^2+(a+\frac{1}{a})x+1=0$.

To do:

We have to solve the given quadratic equation.

Solution:

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

To factorise $x^2+(a+\frac{1}{a})x+1=0$, we have to find two numbers $m$ and $n$ such that $m+n=a+\frac{1}{a}$ and $mn=1(1)=1$.

If $m=a$ and $n=\frac{1}{a}$, $m+n=a+\frac{1}{a}$ and $mn=a\times\frac{1}{a}=1$.

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

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

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

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

$x+a=0$ or $x+\frac{1}{a}=0$

$x=-a$ or $x=-\frac{1}{a}$

The values of $x$ are  $-a$ and $-\frac{1}{a}$.

Tutorialspoint

e

Updated on: 10-Oct-2022

40 Views

Kickstart Your Career

Get certified by completing the course

Get Started