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

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Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink] New post 09 Jun 2012, 17:24
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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] New post 09 Jun 2012, 18:19
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.

[strike]AD[/strike]
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.

Answer is C.
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink] New post 10 Jun 2012, 02:13
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.

Answer: C.

Hope it's clear.
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink] New post 10 Jun 2012, 02:15
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.

Answer: C.

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] New post 13 Jan 2013, 12:30
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)
Hence the answer is NO
Does the equation y = (x – p)(x – q) intercept the x-axis at the   [#permalink] 13 Jan 2013, 12:30
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