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Quadratic equation help

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FindTheLight
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Quadratic equation help
My maths teacher said that to factorise:
I have to change all the signs to make it become:
I see this is his method, however why is this? I usually grasp maths pretty quickly particularly algebra which I enjoy alot, but I can't understand this seemingly random method.
What is the logic behind it? Can anyone explain please?


12112009 02:40 AM 

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random_name
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Re: Quadratic equation help
Pas. Maybe it's just easier with positive numbers?


12112009 02:42 AM 

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FindTheLight
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Re: Quadratic equation help
I know it's easier to factorise with positive numbers, I just don't know why you change the signs. I guess what I'm asking is howcome the signs are changed, it's hard to explain.
I'm not questioning his method, I need to know the logic behind it. Just changing the signs seems like a random thing to do.
He did say it is possible to factorise it anyway without changing the sign. I did this, but he wanted me to do it this way.
Thanks for the reply random


12112009 02:47 AM 

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random_name
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Re: Quadratic equation help
If you left the signs the same, it would become a completely different equation to the one you began with.


12112009 03:11 AM 

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magikarp
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Re: Quadratic equation help
I don't know why you should change the signs, but I'll explain why you can change them, if that's what you're trying to ask.
First, 2x^2 + x + 3 and 2x^2  x  3 aren't equivalent expressions, generally. (For example, if x = 2, the first equals 3 and the second equals 3.)
If you want the expressions to stay equivalent, you can just factor out 1:
2x^2 + x + 3
(2x^2  x 3)
The reason you can just change the signs here, though, without leaving that negative in front, is that to solve a quadratic equation, you'll normally have it so it equals 0.
0 = 2x^2 + x + 3
Then if you divide by 1 (basically, change all the signs) it still equals 0.
0/1 = (2x^2 + x + 3)/1
0 = 2x^2  x  3
That actually applies to other factors too.
0 = 4x^2  2x  6
0/2 = (4x^2  2x  6)/2
0 = 2x^2  x  3
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12112009 03:16 AM 

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FindTheLight
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Re: Quadratic equation help
magikarp Wrote:I don't know why you should change the signs, but I'll explain why you can change them, if that's what you're trying to ask.
First, 2x^2 + x + 3 and 2x^2  x  3 aren't equivalent expressions. (For example, if x = 1, the first equals 1 and the second equals 1.)
If you want the expressions to stay equivalent, you can just factor out 1:
2x^2 + x + 3
(2x^2  x 3)
The reason you can just change the signs here, though, without leaving that negative in front, is that to solve a quadratic equation, you'll normally have it so it equals 0.
0 = 2x^2 + x + 3
Then if you divide by 1 (basically, change all the signs) it still equals 0.
0/1 = (2x^2 + x + 3)/1
0 = 2x^2  x  3
That actually applies to other factors too.
0 = 4x^2  2x  6
0/2 = (4x^2  2x  6)/2
0 = 2x^2  x  3
Ah, I never thought of it like that. Thankyou. That helped alot. Thanks
Thanks for the replies.


12112009 03:38 AM 

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