Find the nature of the roots of the following quadratic equation. If real roots exist,find them:
$2x^2 - 3x + 5 = 0$

(C) For a quadratic equation $ax^2 + bx + c = 0$,the discriminant $D$ is given by $D = b^2 - 4ac$.
$(A)$ If $D > 0$,there are two distinct real roots.
$(B)$ If $D = 0$,there are two equal real roots.
$(C)$ If $D < 0$,there are no real roots.
Given the equation $2x^2 - 3x + 5 = 0$,we compare it with $ax^2 + bx + c = 0$ to get:
$a = 2$,$b = -3$,$c = 5$.
Calculating the discriminant:
$D = b^2 - 4ac = (-3)^2 - 4(2)(5)$
$D = 9 - 40 = -31$.
Since $D < 0$,the given quadratic equation has no real roots.