Question

Part 1: Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation. (4 points)

Part 2: Provide a unique example to back up your explanation. (4 points)

Can someone please help me out? I just don't know how to explain this and it's my last question. (:

Answer 1

so basically we are trying why is b^2 -4ac important in finding the roots..

Answer 2

Good question though.

Answer 3

That's it? It's important for finding roots?

Answer 4

no no, I only stated the formula for the discriminant , .. (b^2 -4ac)

Answer 5

OH lol well, I'm just trying to figure out this part, "and what it tells you about the solutions of a quadratic equation."

Answer 6

one moment

Answer 7

Okay (:

Answer 8

so the discriminant tells you if a trinomial is factorable or not .

If and only if the resulting answer is a perfect square :)

Answer 9

That makes sense, thanks! Can you also help me come up with an example?

Answer 10

Hmmm well I can give you an example but I can't give you a "unique" example. :D

here are some guidelines..

try out some trinomial, or make your own trinomial.

Then solve for the discriminant.

you can tell the purpose of the discriminant by doing that :)

Answer 11

Show your solution and you have an example :)

Answer 12

I'm sorry, but how is a trinomial set up? I am drawing a total blank...I swear I know it

Answer 13

by definition , a trinomial has three terms

hence,

\[ax^2 + b x + c\]

Answer 14

okay thanks! I kept wanting to switch ax^2 and bx lol gimme a sec (:

Answer 15

:)

Answer 16

you can switch it if you want, but to avoid confusion we take the standard form :)

Answer 17

Would this be a good one to work with? I kinda just threw numbers together
2x^2 + 4x + (10)(2)

Answer 18

or you can say,

2x^2 + 4x + 20 :))

Answer 19

lol I yeah I could x]

Answer 20

give it a try :)

Answer 21

Okay hold on (:

Answer 22

*holds on

Answer 23

would it be 4x^2 - 4(4)(20) for the first step? I just want to make sure I am doing it right

Answer 24

The formula for the discriminant is b^2 - 4 a c

where , a b and c are constants :)

Answer 25

Yeah and I plugged them all in. That's how I go 4x^2 - 4(4x)(20)

Answer 26

I'm confusing myself D:

Answer 27

what I mean about constants are,

constants are numbers,
variables are letters

Answer 28

I know that, I'm just lost on what the steps are :l

Answer 29

substitution.

\[ax^2 + bx + c \]

Answer 30

a, b and c are constants :)

Answer 31

you just substitute numbers :) don't plug in variables

Answer 32

and then follow the order of operations , PEMDAS

Answer 33

okay, so my example was was 2x^2 + 4x + 20. The discriminant formula is b^2 - 4(a)(c)
What I don't understand is in the formula, b is squared, but in my example, a is squared. How do I get rid of a^2?

Answer 34

Does that make any sense?

Answer 35

b^2 is indeed the formula.

what is b in your example ?

Answer 36

4

Answer 37

correct then what is (4)^2 ?

Answer 38

what is the value of , (4)^2 - 4 (2) (20) ?

Answer 39

16 - 160?

Answer 40

yep :)

Answer 41

then subtract see if it has a perfect square if not, its not factorable
:)

Answer 42

Would it be -144 or positive 144?

Answer 43

- 144

Answer 44

bigger number always wins the signs when adding and subtracting :)

Answer 45

Just making sure lol so the I would have to multiply the sqrt of -1 times the sqrt of 144 which makes it \[i \sqrt{144}\] right?

Answer 46

And then factor it out since it is a perfect square?

Answer 47

i like the way you think :) go on :)

Answer 48

:D
Okay, so then it would factor out to be sqrt 2 ?

Answer 49

or would it be sqrt 12?

Answer 50

\[i \sqrt{144} = 12i\]

Answer 51

Oops, forgot the i lol

Answer 52

You deserve a medal my friend! :D

Answer 53

thanks haha :) hope you can take care of the rest :)

Answer 54

Yep I can! Thank you so much! You helped out a bunch!

Answer 55

haha :D

Answer 56

don't forget to close the question :)

Answer 57

Okay (: