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, $
3x^2=5x+2
,$ is equivalent to
\begin{align*}
3x^2-5x-2=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, $
3x^2=5x+2
,$ is
\begin{align*}\require{cancel}
&
(-5)^2-4(3)(-2)
\\&=
25+24
\\&=
49
\\&=
7^2
.\end{align*}
Since the discriminant is positive and is a perfect square, then the equation $
3x^2=5x+2
$ 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.
