#### Answer

No real solution; two imaginary solutions

#### Work Step by Step

Compute for the discriminant, $b^2-4ac$
$2x^2 + 5x + 4 = 0$
$a=2$, $b=5$, $c=4$
$b^2-4ac = 5^2-(4⋅2⋅4)$
$b^2-4ac = -7$
Note that the discriminant tells the number and types of solution. If:
$b^2-4ac > 0$: Two unequal real solutions
$b^2-4ac = 0$: One solution (a repeated solution) that is
a real number
$b^2-4ac < 0$: No real solution; two imaginary solutions
The value of the discriminant of the given equation is $-7$, which is $<0$. Therefore, there are no real solution. When solved using the quadratic formula, two imaginary solutions will be obtained .