10.7 Discriminant Discovery!
Let’s do this together:
Step 1: Use the quadratic formula or factoring to find the solutions
0= x2 + 7x - 9
0= x2 + 4x +4
0= x2 + 4x + 6
Step 2:
According to your work above, how many solutions does each equation have (0, 1, or 2)?
0=x2+7x-9
_____
In the quadratic formula x 
0=x2+4x+4
b  b2  4ac
2a
_____
0=x2+4x+6
_____
b2  4ac is called the discriminant
Step 3: Determine whether the discriminant ( b
 4ac ) of each equation is positive, negative or zero.
0=x2+7x-9
________________
2
______________
0=x2+4x+4
0=x2+4x+6
________________
Step 4:
Make a table.
Equation
Number of Solutions
Value of
Discriminant: b  4ac ( pos , neg ,or zero ?)
2
0=x2+7x-9
0=x2+4x+4
0=x2+4x+6
Now Try this with your group:
Step 1: Use the quadratic formula OR factoring to find the solutions
0=x2–6x+9
0=x2 - 6x – 8
0=x2-6x+12
Step 2:
According to your work above, how many solutions does each equation have?
0=x2–6x+9
______
0=x2–6x–7
______
0=x2-6x+12
______
Step 3:
Determine whether the discriminant ( b2  4ac ) of each equation is positive, negative or zero.
0=x2-6x+9 ____________
0=x2-6x–7
______________
0=x2-6x+12 _____________
Step 4:
Make a table.
Equation
0=x2-6x+9
0=x2-6x–7
0=x2-6x+12
Number of Solutions
Value of Discriminant: b2  4ac
Step 5: Make a generalization about the value of the discriminant and the number of solutions of a quadratic
equation:
If discriminant (b2-4ac) is POSITIVE  _____________________________
If discriminant (b2-4ac) is NEGATIVE  _____________________________
If discriminant (b2-4ac) is ZERO  _____________________________
Step 5: Why do you think the pattern always holds true. Think about where the discriminant is located in the
quadratic formula (
) . Write a short paragraph with your group about what is occurring and why.
Practice:
a. find the value of the discriminant and determine the number of solutions to the equations.
b. Based on the value of the discriminant, determine if the equation is factorable.
#1
2x2 + 6x + 5=0
#4
6x2 –x – 4=0
#2
#5
x2 – 7=0
4x2 – 9=0
#3 6x2 – 5x – 4=0
#6 4x2 – 8x + 15=0