1. A quick way to figure out the number of real roots of an equation
The Discriminant
A quick way to figure out the number of real roots of an equation

2. Discriminant?
All it is: the thing under the radical in the quadratic formula
Discriminant, d = b2 – 4ac
Why do we care: If we are only concerned with real roots, this can expedite matters.
Easy because you can do this while in the quadratic formula, so it doesn’t add any steps to the process, just a checkpoint.

3. Using the Discriminant
d = b2 – 4ac
If d > 0, two real roots
If d = 0, 1 real root
If d < 0, no real roots
That’s all.

4. Example 1 x2 + 2x = 12 + 3x First, get in quadratic form
b = -1
c = -12

5. Example 2
x2 – 12x + 36 = 0
a = 1
b = -12
c = 36

6. Example 3
5 x2 – 8x + 9 = 0
a = 5
b = -8
c = 9