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# Data sufficiency roots question

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Senior Manager
Joined: 14 Jul 2006
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27 Jul 2006, 08:48
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Hi guys here is a similar problem to the one I posted yesterday. I tried applying the b^2-4ac equation didnt work out as planned. Please help thanks

How many integers can let x^2+bx+c=0? B and c are constants.
1) c<0
2) b= - (c+1) Dont know why the answer is E

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Senior Manager
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Re: Data sufficiency roots question [#permalink]

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27 Jul 2006, 11:37
apollo168 wrote:
Hi guys here is a similar problem to the one I posted yesterday. I tried applying the b^2-4ac equation didnt work out as planned. Please help thanks

How many integers can let x^2+bx+c=0? B and c are constants.
1) c<0
2) b= - (c+1) Dont know why the answer is E

b^2-4ac = 0 means that it has only one real root.
b^2-4ac = m^2 (where m is integer) means that it has two real roots, but it can be an interger or a rational number

S1. c<0 tells b^2-4c>0 thus, two real roots
x= [-b+-sqrt(b^2-4c)]/2 we don't know x value will be an integer or just areal number. insuff.

S2. b = -(c+1)
x = [c+1+-|c-1|]/2 still insuff. it can be an interger or a rational number
X= c or 1

Combine S1 and S2.. insuff.
X^2-(c+1)X +c = 0
X = [c+1+(1-c)]/2 or [c+1-(1-c)]/2
X = 1 or c (c is just a constant we don't know it's integer or not)
Hence, E.
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Senior Manager
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27 Jul 2006, 11:42
Wow cool now I understand. Thanks a lot

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29 Jul 2006, 14:33
E.
You don't need to use b^2-4ac to arrive at E.
Knowledge of b^2-4ac helps, but is not essential.

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Senior Manager
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29 Jul 2006, 23:50
Hi xsports,

Without using b^2-4ac, how would you resolve this data suff question?

Thanks

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Senior Manager
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Re: Data sufficiency roots question [#permalink]

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30 Jul 2006, 00:00
just use factorization
S1=> straight insufficient
S2=> x^2-(c+1)x+c=0
(x-c)(x-1)=0 => x=1 or c but c can be any number... insufficient
combine S1 and S2 same as above..
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Senior Manager
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30 Jul 2006, 00:06
Thanks a lot. That really helps

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30 Jul 2006, 00:06
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