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Second degree equation

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Second degree equation [#permalink] New post 22 Jan 2011, 16:05
Hello guys,


I have some problem to go from step 1 to step 2

x^2 + 12x -540 = 0 STEP 1

(x-18) (x+30)= 0 STEP 2

I can't find an easy and quick way to solve this problem.
I don't see how you can factor it really fast.
I know that A+B= 12 and AxB= -540 and i know how to do it with b^2-4ac formula, but this takes ages.

If anyone has a tips to factor it fast, I would really appreciated.

THANKS !
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Re: Second degree equation [#permalink] New post 23 Jan 2011, 13:41
Expert's post
etienneb wrote:
Hello guys,


I have some problem to go from step 1 to step 2

x^2 + 12x -540 = 0 STEP 1

(x-18) (x+30)= 0 STEP 2

I can't find an easy and quick way to solve this problem.
I don't see how you can factor it really fast.
I know that A+B= 12 and AxB= -540 and i know how to do it with b^2-4ac formula, but this takes ages.

If anyone has a tips to factor it fast, I would really appreciated.

THANKS !


There is no standard method. It involves using some ingenuity to speed up the process. If nothing works, you could find the prime factors and try combining them in various ways e.g.
A + B = 12
A x B = -540 (Note this is negative which means that one number is -ve and the other is +ve. So you are looking for 2 numbers whose difference is 12 and product is 540)
540 = 2x2x3x3x3x5
I want to combine them such that difference between the numbers is relatively small i.e. 12. So numbers should be close to each other. So I needn't consider combinations like 2 and 2x3x3x3x5 or 5 and 2x2x3x3x3 etc.
I try putting 3x5 together and rest together to get 15 and 36. Difference not 12.
I try putting 3x3x2 together and rest together to get 18 and 30. Difference is 12. Required numbers! Sometimes, it could take time. Its all about practice. GMAT will not give you crazy numbers since it is not a calculation oriented exam.

Using ingenuity could be faster but is more risky. You may get the answer in a few secs or you may not zero in on the answer for a long time. Say 540 = 54*10... Difference is of 44. Too much. We need to get the numbers closer. I take 2 out of 54 and give it to 10 to get 27 and 20. Numbers too close together now. Instead I take 3 out of 54 and give it to 10. I get 18 and 30. The numbers I need!
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Re: Second degree equation [#permalink] New post 24 Jan 2011, 06:23
Thanks !
The decomposition in prime number makes sense.
Re: Second degree equation   [#permalink] 24 Jan 2011, 06:23
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