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Does the curve h(x)=y=ax^2+b intersects the x-axis?

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Kudos [?]: 124 [1], given: 72

GMAT 1: 660 Q46 V35
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Does the curve h(x)=y=ax^2+b intersects the x-axis? [#permalink]

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Does the curve h(x)=y=ax^2+b intersects the x-axis?

Statement 1: h(4)>0
Statement 2: a>0
[Reveal] Spoiler: OA

Kudos [?]: 124 [1], given: 72

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Re: Does the curve h(x)=y=ax^2+b intersects the x-axis? [#permalink]

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New post 31 Jul 2017, 15:53
Hi,

Question :

Does the curve h(x)=y=ax^2+b intersects the x-axis?

Basically its a parabola equation.

For any parabola, ax2 + bx + C = 0, it will intersect the x axis only if discriminant b2-4ac = 0.

it wont intersect x axis if b2- 4ac<0;

Coming to the question:

y = ax2 + b
dicriminant = -4ab ;
now our aim is to check whether -4ab (discriminant in the given equation) is less than, equal or greater than 0.
1) h(4)>0 = > 16a+b>0 = >from this we cannot say about a & b
we dont know whether a and b is + ve or -ve.

So insuff

2) a>0
so we now have a(>0), but we dont know the value of b.

So insuff.


Combining 1 & 2
16a + b > 0
& a>0

therefore we can infer that b >0

so our discriminant -4ab<0

so it dont have any x intercepts.

Suff

C

Regards
Raju

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Re: Does the curve h(x)=y=ax^2+b intersects the x-axis? [#permalink]

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New post 31 Jul 2017, 21:43
gvvsnraju@1 wrote:
Hi,

Combining 1 & 2
16a + b > 0
& a>0

therefore we can infer that b >0

so our discriminant -4ab<0


what if a = 1 and b = -2

Kudos [?]: [0], given: 20

Re: Does the curve h(x)=y=ax^2+b intersects the x-axis?   [#permalink] 31 Jul 2017, 21:43
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