Question

The roots of the equation $x^2-2\sqrt{2}x+1=0$ are-

• A. real and distinct
• B. imaginary and different
• C. real and equal
• D. rational and different

Answer 1

Answer: (A)

real and distinct

To find the nature of the roots we have to find the discriminant value.

Discriminant, $D=b^2-4ac$

On comparing the given equation with the general equation that is : $a{x}^2+bx+c=0$

We get , $a=1$ , $b=8^{1/2}$ and $c=1$

So, now $D=(8^{1/2}{)}^2-4\times 1\times 1$

$D=8-4=4>0$

As we can see that the discriminant value is greater than $0$.

Therefore,the roots are real and distinct.