Question

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2-\left(\sqrt{2}+1\right)x+\sqrt{2}=0$

Answer 1

We have been given that,

Now take the constant term to the RHS and we get

Now add square of half of co-efficient of ‘x’ on both the sides. We have,

Since RHS is a positive number, therefore the roots of the equation exist.

So, now take the square root on both the sides and we get

Now, we have the values of ‘x’ as

Also we have,

Therefore the roots of the equation are and.