Answer:
[tex]\large \boxed{\text{Zero}}[/tex]
Step-by-step explanation:
x² - 3x + 5 = 0
ax² + bx + c = 0
a = 1; b = -3; c = 5
The expression b² - 4ac is called the discriminant (D). We can use its value to give us the number of real roots,
[tex]D = \begin{cases}\text{positive} & \quad \text{2 real solutions}\\\text{zero} & \quad \text{1 real solution}\\\text{negative} & \quad \text{0 real solutions}\\\end{cases}[/tex]
[tex]D &= &b^2 - 4ac= (-3)^2 - 4 \times 1\times 5= 9 - 20=-11\end{array}\\\text{The sign of D is negative, so there are $\large \boxed{\textbf{zero}}$ real solutions.}[/tex]
The figure below shows that the graph of your quadratic never reaches the x-axis, so there are no real roots.
