#### Answer

Choice C

#### Work Step by Step

Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
H(x)=2x^2-7x-4
,$ is equivalent to
\begin{array}{l}\require{cancel}
H(x)=(2x+1)(x-4)
.\end{array}
Equating $H(x)$ to $0,$ then
\begin{array}{l}\require{cancel}
0=(2x+1)(x-4)
.\end{array}
Equating each factor to zero (Zero Product Property) then the zeroes of the equation above are $
x=\left\{ -\dfrac{1}{2},4 \right\}
.$ Hence, $\text{
Choice C
.}$