State whether the quadratic equation $2 x^{2}-6 x+\frac{9}{2}=0$ has two distinct real roots. Justify your answer.

(B) The given quadratic equation is $2 x^{2}-6 x+\frac{9}{2}=0$.
Comparing this with the standard form $a x^{2}+b x+c=0$,we get:
$a=2, b=-6, c=\frac{9}{2}$.
To determine the nature of the roots,we calculate the discriminant $D = b^{2}-4ac$:
$D = (-6)^{2} - 4(2)(\frac{9}{2})$
$D = 36 - 36 = 0$.
Since the discriminant $D = 0$,the quadratic equation has two equal real roots. Therefore,it does not have two distinct real roots.