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

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A curve is represented by y=ax^2+2bx+c. How many real roots [#permalink]  22 Jul 2008, 05:19
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
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Schools: INSEAD Class of July '10
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Re: PARABOLA [#permalink]  22 Jul 2008, 05:30
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, 05:30
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