State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

(A) Given,the quadratic equation is $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x+\frac{1}{\sqrt{2}}=0$.
On comparing this with the standard form $ax^{2}+bx+c=0$,we get:
$a=\sqrt{2}$,$b=-\frac{3}{\sqrt{2}}$,and $c=\frac{1}{\sqrt{2}}$.
The discriminant $D$ is given by $D = b^{2}-4ac$.
Substituting the values:
$D = \left(-\frac{3}{\sqrt{2}}\right)^{2} - 4(\sqrt{2})\left(\frac{1}{\sqrt{2}}\right)$
$D = \frac{9}{2} - 4$
$D = \frac{9-8}{2} = \frac{1}{2}$.
Since $D = \frac{1}{2} > 0$,the discriminant is positive.
Therefore,the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x+\frac{1}{\sqrt{2}}=0$ has two distinct real roots.