# History Trivia: Fannie Lou Hamer: First African American Woman Delegate at DNC

Wonder Woman... Black Widow... Fannie Lou Hamer... Yeah, it's kind of got that superhero ring to it, doesn't it?

 Language English Language Social Studies Famous BiographiesHistory TriviaU.S. History

### Transcript

00:20

The discriminant determines the nature and number of solutions of a quadratic equation.

00:25

If b2 – 4ac is positive and greater than zero, there will be two distinct, real solutions. [2 real solutions appear from the magic discriminant ball]

00:34

If b2 – 4ac is zero, there will be one distinct, real solution. [1 real solution appears from the magic discriminant ball]

00:39

But, if b2 – 4ac is negative and less than zero, there are no real solutions.

00:46

Let's get quadratic for a couple of examples.

00:49

Our first example is x-squared plus three-x plus five equals zero. [The equation is written out]

00:54

Plugging these bad boys into the discriminant, b squared minus 4ac, we get three-squared

01:00

minus four-times-one-times-five.

01:04

This simplifies to nine minus twenty, which is negative eleven.

01:08

This is less than zero…so there are no real solutions. [Guy holding his arms up]

01:14

What does “no real solutions” mean? [Students in class]

01:16

If we take a look at the graph, the parabola does not touch the x-axis at any x-value. [Finger going along the x-axis]

01:22

So it's not real, it doesn't exist.

01:25

For our second example, we have the equation...

01:27

x-squared minus six-x minus ten equals zero. [The equation is written out]

01:31

Plugging this into the discriminant it looks like...

01:34

six-squared minus four times negative-ten times one.

01:39

This is thirty-six plus forty, which is seventy-six.

01:43

Seventy-six is greater than zero.

01:46

So there are two distinct, real solutions to this problem. [Guy looks happy]

01:51

By looking at the graph, we can see that there are two real solutions because the parabola [Arrows point to the solutions on the graph]

01:56

touches the x-axis at two distinct x-values.

02:01

Okay, so the Magic Discriminant Ball might not be able to help you with some of life's [Guy asking the ball a random question]

02:05

biggest questions… [The magic discriminant ball looks angry]

02:07

… but using the discriminant can help you ace your next math test. [Guy looks happy as he gets an A+ on his test]