# What is a quadratic polynomial?

#### eddy2017

##### Senior Member
A quadratic equation takes this form: ax^2+bx+c=0
I don't think any of the equations in this post follow this pattern, right?. Or do they?. They are not equaled to 0. These are ploynomials. Just wondering in case these can be solved as a Q.E

#### eddy2017

##### Senior Member
(2x+ *)^2 = (2x)^2 + 2(2x)(*) + (*)^2 = 4x^2 + 4x* + *^2 = 4x^2 + 12xy + 9y^2

You need 4x* = 12xy. Divide by sides by 4x to get * = ...
Easy
*= 3y

#### mmm4444bot

##### Super Moderator
Staff member
Who is 'we', and what post are you talking about? Or, were you just thinking out loud about something that doesn't really matter in this thread.

#### eddy2017

##### Senior Member
Who is 'we', and what post are you talking about? Or, were you just thinking out loud about something that doesn't really matter in this thread.

Oh, the tutors were discussing that I should learn about quadratic equations in a post I made. I saw this post and I want to know if any of the equations here qualify as quadratic. That is what I said we( referring to the tutors and me ). Take a look at my post here #10. I hope I am not breaking any rules.

#### mmm4444bot

##### Super Moderator
Staff member

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#### eddy2017

##### Senior Member

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One question, mmm. Just to be sure I don't mess up.
Am I allowed to reply to other threads?. Or just the tutors?. Please I need to know this. I didn't read anything about not being able to in the guidelines, but just to be on the safe side. I'd like to know your opinion

#### mmm4444bot

##### Super Moderator
Staff member
You're free to comment, but not for the purposes of starting your own discussions. If you're looking for tutoring on your own questions (like, what is or isn't a quadratic polynomial), then please start your own threads.

As far as trying to help other students, I wish you wouldn't. In the past, you've posted misinformation or off-topic information in other people's threads.

Thanks for understanding!

#### eddy2017

##### Senior Member
I understand. And yes, you are right!. Thanks.

#### Otis

##### Elite Member
A quadratic equation takes this form: ax^2+bx+c=0
That is one specific form, Eddy, but there are many other quadratic forms.

The exercise you've quoted is not about quadratic equations. It concerns quadratic polynomials and special factoring patterns.

Remember also: a quadratic polynomial may contain more than one variable.

#### Jomo

##### Elite Member
3x^4 + 2x^2 - 11 = 0 is a quadratic equation in x^2.

#### Otis

##### Elite Member
Another example:

x^2 = x^2

Not really a quadratic equation. Agree?

#### Jomo

##### Elite Member
Agree. A quadratic equation has exactly two solutions.

#### Otis

##### Elite Member
Another perspective: all quadratic equations in one variable may be put in the form

ax^2 + bx + c = 0

But equations like

x^2 - x - 12 = (x - 4)(x + 3)

may not be put in that form. Hence, they are not quadratic equations. They are identities.

#### Otis

##### Elite Member
Just wondering in case these can be solved as a Q.E
They aren't asking you to solve equations for any variable(s), Eddy. They're asking you to find a value for each unknown parameter (i.e., the numbers represented by asterisks).

#### eddy2017

##### Senior Member
They aren't asking you to solve equations for any variable(s), Eddy. They're asking you to find a value for each unknown parameter (i.e., the numbers represented by asterisks).

That is fairly easy. At least I was able to do number 1.

#### eddy2017

##### Senior Member
Agree. A quadratic equation has exactly two solutions.
Prof Steven, seconding your reply that a QE has two solutions I have found this statement:
"A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.
Can you provide an example where this can be seen?.
Why two solutions?

#### lev888

##### Elite Member
Prof Steven, seconding your reply that a QE has two solutions I have found this statement:
"A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.
Can you provide an example where this can be seen?.
Why two solutions?
When is product ab = 0?

#### eddy2017

##### Senior Member
When is product ab = 0?
when one of the factors is equal to zero.
Either a or b

Last edited:

#### lev888

##### Elite Member
when one of the factors is equal to zero.
Either a or b
So when we have a product of 2 linear factors equal to 0, either one can be 0 -> 2 solutions.

#### eddy2017

##### Senior Member
So when we have a product of 2 linear factors equal to 0, either one can be 0 -> 2 solutions.
Thanks, prof.