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Quadratic DS

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Source: — Data Sufficiency |
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Re: Quadratic DS

by iamcste » Thu May 21, 2009 3:07 am
aj5105 wrote:How many points does the curve represented with y= intersect with axis-x?

(1) b>a
(2) c<0
let me try

For a quadratic ax^2+bx+c, b^2>4ac to have real roots..( Not complex roots)

Individually we dont have info about a,b and c in either statement so cancel, A.B and D


Together,

b=3, a=2, c=-1, b^2>4ac..2 real roots..Sufficient

B=3, a=-4, c=-1, b^2<4ac..we can have complex roots here..Insuff

Choose E
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by aj5105 » Thu May 21, 2009 3:26 am
OA [spoiler](E)[/spoiler]
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by mike22629 » Thu May 21, 2009 10:02 am
just use discriminate formula

That tells you whether quadratic formula crosses x-axis
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by Vemuri » Thu May 21, 2009 11:09 am
mike22629 wrote:just use discriminate formula

That tells you whether quadratic formula crosses x-axis
Can you elaborate what a discriminate formula is? The way I sythesized the question is:

y=ax^2+bx+c ==> ax^2+bx+c = 0 (y=0 when it passes through x axis)

The roots of the above equation are: (-b+-sqrt(b^2-4ac))/2a

I got lost on how to use the statements on the 2 roots above. Any help?
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by aj5105 » Thu May 21, 2009 11:14 am
Check iamcste's solution and also the doc i have attached. It might help.

Vemuri wrote:
mike22629 wrote:just use discriminate formula

That tells you whether quadratic formula crosses x-axis
Can you elaborate what a discriminate formula is? The way I sythesized the question is:

y=ax^2+bx+c ==> ax^2+bx+c = 0 (y=0 when it passes through x axis)

The roots of the above equation are: (-b+-sqrt(b^2-4ac))/2a

I got lost on how to use the statements on the 2 roots above. Any help?
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by iamcste » Thu May 21, 2009 11:16 am
[quote="VemuriThe roots of the above equation are: (-b+-sqrt(b^2-4ac))/2a

I got lost on how to use the statements on the 2 roots above. Any help?[/quote]

In the formula, b^2-4ac controls the nature of roots.

There are 3 situations depending on the b^2-4ac part

1. b^2=4ac, roots are equal and real..In this case there is just one intersection with x axis

2. b^2>4ac, 2 real roots and hence there are 2 points at which curve would intersect x-axis

3. b^2<4ac, we will have 2 complex roots

so our job from 2 statements is to check whether we have one of the cases from the above depending on the value of a, b and c

clearly either of statements do not talk about a, b and c

hence its C or E qtn

Referring to my post earlier, based on relations and information provided by the statement, there could be more than one cases possible that is we cant answer in one of the 3 possible cases

Insufficient

Choose E

HTH
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IMO

by kc_raj » Sat May 23, 2009 2:48 pm
IMO E

because 4ac could be negative or positive, information not sufficient to tell weather it has two real roots or none or only one real root
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