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Manager  S
Joined: 15 Jul 2016
Posts: 93
GMAT 1: 690 Q48 V36 Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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Hi All,

can somebody please help me understand this? Here, when we get (x-a)(x-b) = 0, then why aren't the roots x=a and x=b ?

Then statement 1 will be sufficient ?

VeritasKarishma Bunuel egmat chetan2u
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Math Expert V
Joined: 02 Sep 2009
Posts: 58117
Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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578vishnu wrote:
Hi All,

can somebody please help me understand this? Here, when we get (x-a)(x-b) = 0, then why aren't the roots x=a and x=b ?

Then statement 1 will be sufficient ?

VeritasKarishma Bunuel egmat chetan2u

This is a value question, which means that for a statement(s) to be sufficient you need to get single numerical value of the intersect points.
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Manager  S
Joined: 15 Jul 2016
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GMAT 1: 690 Q48 V36 Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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Bunuel wrote:
578vishnu wrote:
Hi All,

can somebody please help me understand this? Here, when we get (x-a)(x-b) = 0, then why aren't the roots x=a and x=b ?

Then statement 1 will be sufficient ?

VeritasKarishma Bunuel egmat chetan2u

This is a value question, which means that for a statement(s) to be sufficient you need to get single numerical value of the intersect points.

Hi Bunuel

I agree. However once we get x=a,b
I used this info in st 1

a+b = -1

Since a=x and b=x

X+x = -1
x= -1/2

I know what I’m doing is not right but theoretically I cannot seem to understand why this approach is incorrect

Thanks

Posted from my mobile device
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Math Expert V
Joined: 02 Sep 2009
Posts: 58117
Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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1
578vishnu wrote:
Bunuel wrote:
578vishnu wrote:
Hi All,

can somebody please help me understand this? Here, when we get (x-a)(x-b) = 0, then why aren't the roots x=a and x=b ?

Then statement 1 will be sufficient ?

VeritasKarishma Bunuel egmat chetan2u

This is a value question, which means that for a statement(s) to be sufficient you need to get single numerical value of the intersect points.

Hi Bunuel

I agree. However once we get x=a,b
I used this info in st 1

a+b = -1

Since a=x and b=x

X+x = -1
x= -1/2

I know what I’m doing is not right but theoretically I cannot seem to understand why this approach is incorrect

Thanks

Posted from my mobile device

x-intercepts of a parabola y = (x + a)(x + b) are x = -a and x = -b. This does not mean that -a = -b. For example, The x-intercepts of y = (x + 1)(x + 2) are x = -1 and x = -2.
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Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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2
578vishnu wrote:
Bunuel wrote:
578vishnu wrote:
Hi All,

can somebody please help me understand this? Here, when we get (x-a)(x-b) = 0, then why aren't the roots x=a and x=b ?

Then statement 1 will be sufficient ?

VeritasKarishma Bunuel egmat chetan2u

This is a value question, which means that for a statement(s) to be sufficient you need to get single numerical value of the intersect points.

Hi Bunuel

I agree. However once we get x=a,b
I used this info in st 1

a+b = -1

Since a=x and b=x

X+x = -1
x= -1/2

I know what I’m doing is not right but theoretically I cannot seem to understand why this approach is incorrect

Thanks

Posted from my mobile device

In addition to what Bunuel said above, think in this way too:

When we have (x + a)(x + b) = 0, x is a variable and a and b are some constant values.

We know that x must take one of two values: -a or -b
x must be either -a or -b so that the product becomes 0.

When you say a = -x, and b = -x, you are assuming that a and b are equal and their value is some constant -x (which is not the case)

e.g.
(x + 2)(x - 1) = 0 implies x is either -2 or 1. Can I say that -2 = x and 1 = x so (-2 + 1) = x + x = -1?
This gives us x = -1/2 but we know that x is either -2 or 1. Then this is not possible. Our assumption here is that a and b are equal which they needn't be.
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Manager  S
Joined: 15 Jul 2016
Posts: 93
GMAT 1: 690 Q48 V36 Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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Thankyou Bunuel and VeritasKarishma

It's clear now _________________
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Intern  Joined: 18 May 2019
Posts: 2
Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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I stopped when I had two equation involving A&B thinking A and B will have multiple answer and close E.

For DS do we always need to find complete solution bec looking at the equation one might interpret that this equation would have multiple ans hence information is not sufficient.

udaymathapati wrote:
Attachment:
M-Q19.JPG

At what two points does the graph of y = (x+a)(x+b) intersect the x axis?

You don't need to worry what the equation represents. Just think, what does 'intersection with x axis' imply? It means the y co-ordinate is 0.

0 = (x+a)(x+b)
or x = -a or -b
Hence the graph must intersect the x axis at points (-a, 0) and (-b, 0). We need the values of a and b now.

Statement 1: a + b = -1
Two variables, only one equation. Not sufficient.

Statement 2: Graph intersects the y axis at (0, -6).
At y axis, x = 0. This means when x = 0, y co-ordinate is -6.
Put these values in y = (x+a)(x+b) to get -6 = ab.
Again, two variables, one equation. Not sufficient alone.

Using both statements, we have two variables and two different equations so we will be able to find the values of a and b. It doesn't matter which is 'a' and which is 'b'. We find that the two of them are -3 and 2. Since we need the points (-a, 0) and (-b, 0), the required points are (3, 0) and (-2, 0). Sufficient.

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Joined: 03 Jun 2019
Posts: 1525
Location: India
Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)  [#permalink]

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misterJJ2u wrote:
In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

(1) a + b = -1
(2) The graph intersects the y-axis at (0, -6)

Asked: In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

At x = -a & at x = -b, the graph intersect x-axis.

(1) a + b = -1
Multiple values of a & b satisfy the condition.
NOT SUFFICIENT

(2) The graph intersects the y-axis at (0, -6)
At x = 0 ; y=ab = -6
ab = -6
Multiple values of a & b satisfy the condition
NOT SUFFICIENT

(1) + (2)
(1) a + b = -1
(2) The graph intersects the y-axis at (0, -6)
ab = -6
b = -a -1
a(a+1) =6
a = 2 or -3
(a, b) = {(2,-3),(-3,2)}
The graph intersects x-axis at x=3 & x=-2
SUFFICIENT

IMO C
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E-mail : kinshook.chaturvedi@gmail.com Re: In the xy-plane, at what two points does the graph of y=(x+a)(x+b)   [#permalink] 16 Sep 2019, 07:36

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