Answer
Discriminant: $
-35
$
Number of Real Solutions: $
0
$
Number of Imaginary Solutions: $
2
$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
3x^2-x+3=0
,\end{align*} has $a=
3
,$ $b=
-1
,$ and $c=
3
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}\require{cancel}b^2-4ac&\Rightarrow
(-1)^2-4(3)(3)
\\&=
1-36
\\&=
-35
.\end{align*}
Since the value of the discriminant is less than $0,$ then there are $2$ imaginary solutions.
