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# Does the equation y = (x – p)(x – q) intercept the x-axis at

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Manager
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Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink]  09 Jun 2012, 16:24
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Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

(1) pq = -8

(2) -2 – p = q
[Reveal] Spoiler: OA

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Re: coordinate [#permalink]  09 Jun 2012, 17:19
y=(x-p)(x-q)

Basically, when y=0 and x=2, does equation balance?

0 = (2-p)(2-q)
0 = 4-2q-2p+qp

In order to know this, we need to know q & p

1) pq = -8
This only tell us p or q, but not both.

BCE

2) -2 - p = q
This only tell us p or q, but not both.

1+2) We can determine both p & q through these two independent equations.

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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink]  10 Jun 2012, 01:13
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Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts are $$(p, 0)$$ and $$(q, 0)$$. The question basically asks whether either $$p$$ or $$q$$ equals 2.

(1) pq = -8. Not sufficient to say whether p or q equals 2.

(2) -2 – p = q. Not sufficient to say whether p or q equals 2.

(1)+(2) Solving $$pq=-8$$ and $$-2-p=q$$ gives us that either $$p=-4$$ and $$q=2$$ OR $$p=2$$ and $$q=-4$$. In ether case one of the unknowns is 2, so $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient.

Hope it's clear.
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Senior Manager
Joined: 13 Jan 2012
Posts: 306
Weight: 170lbs
GMAT 1: 730 Q48 V42
GMAT 2: 740 Q48 V42
WE: Analyst (Other)
Followers: 9

Kudos [?]: 95 [1] , given: 38

Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink]  10 Jun 2012, 01:15
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Bunuel wrote:
Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts are $$(p, 0)$$ and $$(q, 0)$$. The question basically asks whether either $$p$$ or $$q$$ equals 2.

(1) pq = -8. Not sufficient to say whether p or q equals 2.

(2) -2 – p = q. Not sufficient to say whether p or q equals 2.

(1)+(2) Solving $$pq=-8$$ and $$-2-p=q$$ gives us that either $$p=-4$$ and $$q=2$$ OR $$p=2$$ and $$q=-4$$. In ether case one of the unknowns is 2, so $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient.

Hope it's clear.

Damn, you're good! Was my approach right at all? Sometimes I wish a had an identical twin who could just get a 50 on my Quant section for me while I do the Verbal section, haha.
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Does the equation y = (x – p)(x – q) intercept the x-axis at the [#permalink]  13 Jan 2013, 11:30
C.

If y = 0,

this reduces to a quadratic equation.
sum of roots = 2, product of roots = -8.
Thus the roots are 4 and -2.
Line passes through (4,0) and (-2,0)
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink]  27 Jan 2014, 17:23
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at   [#permalink] 27 Jan 2014, 17:23
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