The discriminant of the quadratic equation $2x^2 + 5x + c = 0$ is 1. The value of $c$ is:

Given,

Quadratic equation : $2x^2 + 5x + c = 0$

Comparing with $ax^2 + bx + c = 0$,

$a = 2, b = 5, c = c$

By formula,

Discriminant (D) = $b^2 - 4ac$

$$\begin{aligned}\Rightarrow 1 = 5^2 - 4 \times 2 \times c \\[1em] \Rightarrow 1 = 25 - 8c \\[1em] \Rightarrow 8c = 25 - 1 \\[1em] \Rightarrow 8c = 24 \\[1em] \Rightarrow c = 3.\end{aligned}$$

Hence, option 4 is the correct option.