Given a quadratic function of the
form
or a
quadratic equation of the form 
the discriminant is the value of
When Do We Use the Discriminant?
The value of the discriminant tells us the number
of solutions to a quadratic equation of the form . Also, it tells us
the number of times that the relative function 
intersects the x axis. For this we use the following
analysis.
Number of solutions |
Graphical Implication |
|
If  > 0 |
2 |
Relative function hits the x axis twice. |
If  = 0 |
1 |
Relative function hits the x axis once. |
| If < 0 |
0 |
Relative function does not hit the x axis. |
1. Identify a, b & c.
2 Plug them into the discriminant and simplify the expression.
3. Use the table above to state the number of solutions to the equation or the number of places the relative function crosses the x axis.
Directions: Please use the discriminant to state the number of real solutions to the following equations.
Step 1
a = 3, b= -4 & c=2
Step 2
(-4)2-4(3)(2)
16-12(2)
16-24
-8
Step 3
-8 < 0
This implies that there are no real solutions to the given equation.
Also, it implies that the graph of the relative function does not intersect the x axis.
Problems that You Should Practice
Directions: Please use the discriminant to state the number of real solutions to the following equations.
