Answer
discriminant: 64
number of solution: Choice A
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
4t^2=3-4t
,$ is equivalent to
\begin{align*}
4t^2+4t-3&=0
.\end{align*}
The equation above has
\begin{align*}a=
4
,b=
4
,\text{ and }c=
-3
.\end{align*}
Using $
b^2-4ac
$ or the discriminant, then
\begin{align*}
b^2-4ac&\Rightarrow
4^2-4(4)(-3)
\\&=
16+48
\\&=
64
.\end{align*}
Since the discriminant is $
64
$ (which is a positive and a perfect square number, since $64=8^2$), then the solutions of the given equation are two rational numbers (Choice A).
