Solve the following quadratic equations by factorization:

Question:

Solve the following quadratic equations by factorization:

$\frac{2}{x^{2}}-\frac{5}{x}+2=0$

Solution:

We have been given

$\frac{2}{x^{2}}-\frac{5}{x}+2=0$

Now we solve the above quadratic equation using factorization method.

Therefore,

$\frac{2-5 x+2 x^{2}}{x^{2}}=0$

$2 x^{2}-5 x+2=0$

$2 x^{2}-4 x-x+2=0$

$2 x(x-2)-1(x-2)=0$

 

$(2 x-1)(x-2)=0$

Now, one of the products must be equal to zero for the whole product to be zero. Hence we equate both the products to zero in order to find the value of x.

Therefore,

$2 x-1=0$

$2 x=1$

$x=\frac{1}{2}$

Or

$x-2=0$

 

$x=2$

Hence, $x=\frac{1}{2}$ 아 $x=2$.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now