Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 18:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A curve is represented by y=ax^2+2bx+c. How many real roots

Author Message
Current Student
Joined: 11 May 2008
Posts: 556
Followers: 8

Kudos [?]: 190 [0], given: 0

A curve is represented by y=ax^2+2bx+c. How many real roots [#permalink]

### Show Tags

22 Jul 2008, 06:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A curve is represented by y=ax^2+2bx+c. How many real roots does the equation ax^2+2bx+c=0 have?
(1) a < 0
(2) b^2 > c
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 8

Kudos [?]: 56 [0], given: 0

### Show Tags

22 Jul 2008, 06:30
Discriminant of this polynomial function is $$\Delta = (2b)^2 - 4 a c = 4(b^2-ac)$$

If $$\Delta>0$$: 2 real roots
If $$\Delta=0$$: 1 real root
If $$\Delta<0$$: 0 real root

So we just have to loof at the sign of $$b^2-ac$$

(1) doesn't give us any information about b and c and is therefore insufficient

(2) doesn't give us any information about a and is therefore insufficient

(1) and (2) together are insufficient too:
let's set $$b=1$$ and $$c=-1$$ (it verifies $$b^2>c$$): we then have $$\Delta = 1+a$$

If $$a>-1$$: 2 real roots
If $$a=-1$$: 1 real root
If $$a<-1$$: 0 real root

Re: PARABOLA   [#permalink] 22 Jul 2008, 06:30
Display posts from previous: Sort by