### The Discriminant

b^2-4ac in the quadratic equation:

-b+(b^2-4ac)

- _______

2a

(pretend these parenthesis are the square root)

is what you called "the discriminant". The discriminant helps you to find how many real solutions a quadratic equation has without solving the equation or graphing.

ex: x^2 - x - 12 = 0

substitute the value of discriminant from the equation like this:

b^2-4ac

(-1)^2 - 4(1)(-12)= 49

which means it has 2 real no. solutions because the answer is greater than 1.

another example: x^2 - x + 2 = 0

let's substitute it again in the discriminant like this:

b^2-4ac

(-1)^2 - 4(1)(2)= -7

which means it has 0 real no. solution because tha answer is a negative no. or less than 1.

I'll give you one more example and i'll explain things to you more so you can understand(I hope I could do that).

ex: x^2 - 6x + 9 = 0

use the discriminate formula which is:

b^2-4ac

(-6)^2 - 4(1)(9)= 0

which means it has only 1 real no. because the anwer is 0.

Explanation:

The ff. should be keep in mind in order to understand how many roots and what kind of roots(irrational or rational or imaginary) does a quadratic function has:

1.)If the answer to the discriminant formula that we just did is > 0(greater than zero)and it's a non-perfect square then the equation has 2 real irrational roots.

2.)If the answer to the discriminant formula is also > 0(greater than zero) and it's a perfect square then the equation has 2 real rational roots.

3.)If the answer to the discriminant formula is = 0(equals to zero) then the equation has 1 real no. root.

4.)If the answer to the discriminant formula is <0(less than zero) then the equation has 0 real number roots but the roots are called the "imaginary numbers or roots".

That's all...whew!I already made my first post being a scribe tonight.I promise Mr. M to make one this night. Don't forget to study guys we do have a quiz tomorrow morning so good luck!my next scribe is..I'll tell you tom. ok?see yah!

## 2 Comments:

You have done a

GREATjob...in complicating a simple topic. Your long sentences cause confusion. As for the numbered stuff, it is just the table at the back of the book. putting the table would've been more efficient and easier to understand...

PLEASE use a superscript tag... using "^" is a lazy way of doing exponents... This had been posted before in the blog that instead of using ^, use superscript tag [sup]

text[/sup]...7:06 AM

Err.. Albert, you didn't pick the scribe for today. Please pick one to avoid the confusion.

8:15 PM

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