Answer
two complex but not real solutions
Work Step by Step
Using the properties of equality, the given quadratic equation, $
5-4x+12x^2=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
12x^2-4x+5=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
12
\\b=
-4
\\c=
5
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(-4)^2-4(12)(5)
\\\\=
16-240
\\\\=
-224
.\end{array}
Since the value of the discriminant is $\text{
less than zero
,}$ then the given quadratic equation has $\text{
two complex but not real solutions
}$.
