Data sufficiency roots question

Question

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

freetheking · Answer

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=  /2 we don't know x value will be an integer or just areal number. insuff.

S2. b = -(c+1)
x =  /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 =  /2 or  /2
X = 1 or c (c is just a constant we don't know it's integer or not)
Hence, E.

apollo168 · Answer

Wow cool now I understand. Thanks a lot :-D

xsports · Answer

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

apollo168 · Answer

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

freetheking · Answer

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..

apollo168 · Answer

Thanks a lot. That really helps :-D

Data sufficiency roots question

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