Answer
Choice A;
can be solved using the Zero-Factor Property
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
4x^2=4x+3
,$ is equivalent to
\begin{align*}
4x^2-4x-3=0
.\end{align*}
The discriminant of a quadratic equation $ax^2+bx+c=0,$ is given by $b^2-4ac$. Thus, the discriminant of the given equation, $
4x^2=4x+3
,$ is
\begin{align*}\require{cancel}
&
(-4)^2-4(4)(-3)
\\&=
16+48
\\&=
64
\\&=
8^2
.\end{align*}
Since the discriminant is positive and is a perfect square, then the equation $
4x^2=4x+3
$ has two rational numbers as solutions or $\text{
Choice A
}$.
Furthermore, since the coefficients of the given equation are integers and the discriminant is a perfect square, then the given equation can be solved using the Zero-Factor Property.