(x + a)(x + b)

Question

In the xy plane, at what point does y = (x + a)(x + b) cross the x axis? a. a + b = -1 b. graph intersects y axis at (0, -6) Don't have OA. IMO : C

Brent@GMATPrepNow · Answer

piyush_nitt wrote:In the xy plane, at what point does y = (x + a)(x + b) cross the x axis?
a. a + b = -1
b. graph intersects y axis at (0, -6)
Don't have OA. IMO : C

To begin, let's look at the point where a line (or curve) crosses the x-axis. At the point of intersection the point is on the x-axis, which means that the y-coordinate of this point equals 0.

Aside: To find where the line y=2x+3 crosses the x-axis, we let y=0 and solve for x. We get: 0=2x+3 --> x=-3/2. So, the point of intersection is (-3/2, 0)

So, to determine the point where y = (x + a)(x + b) crosses the x axis, let y=0 and solve for x.
We get: 0 = (x + a)(x + b), which means x=-a, x=-b
So, to solve this question, we need the value of a and b

(1) a+b = -1 INSUFFICIENT (many solutions for a and b)
(2) this tells us that when x=0 y=-6
If we plug x=0 and y=-6 into the equation, we get -6 = (0 + a)(0 + b), which tells us that ab=-6 INSUFFICIENT (many solutions for a and b)

(1) & (2) if a+b = -1 and ab=-6, then we can determine that either a=-3 and b=2 or a=2 and b=-3
Both sets of solutions yield the x-intercepts as (2,0) and (-3,0), so we have enough information.

Note: Since there are two x-intercepts, the question should have read "at what points does y = (x + a)(x + b) cross the x axis?"

Brent Hanneson - Creator of GMATPrepNow.com

fercho81 · Answer

Hey man, this is another version of the anwer in case you are interested https://www.beatthegmat.com/gmat-prep-xy ... tml#147608

Pdgmat2010 · Answer

Hello Brent,
Just had a question regarding the equations of lines in general

1. since y = (x+a)(x+b) , this means that this is a 2nd degree equation and hence x should have 2 values. i.e. 2 solutions.

2.i got confused when i reached the point ab=-6 and a+b=-1
question stem : at what point does the line intersect the x-axis?
my soln : 2 points possible (2,0) and (-3,0) so i chose E ( as 1 single soln didnt present itself)

it was only after seeing the explanations that i realised that i probably should not have taken the wording too literally
and should have chosen C ( for reasons mentioned in point 1)

your comments pls?

Cheers,
pd

Brent Hanneson wrote:
piyush_nitt wrote:In the xy plane, at what point does y = (x + a)(x + b) cross the x axis?
a. a + b = -1
b. graph intersects y axis at (0, -6)
Don't have OA. IMO : C
To begin, let's look at the point where a line (or curve) crosses the x-axis. At the point of intersection the point is on the x-axis, which means that the y-coordinate of this point equals 0.

Aside: To find where the line y=2x+3 crosses the x-axis, we let y=0 and solve for x. We get: 0=2x+3 --> x=-3/2. So, the point of intersection is (-3/2, 0)

So, to determine the point where y = (x + a)(x + b) crosses the x axis, let y=0 and solve for x.
We get: 0 = (x + a)(x + b), which means x=-a, x=-b
So, to solve this question, we need the value of a and b

(1) a+b = -1 INSUFFICIENT (many solutions for a and b)
(2) this tells us that when x=0 y=-6
If we plug x=0 and y=-6 into the equation, we get -6 = (0 + a)(0 + b), which tells us that ab=-6 INSUFFICIENT (many solutions for a and b)

(1) & (2) if a+b = -1 and ab=-6, then we can determine that either a=-3 and b=2 or a=2 and b=-3
Both sets of solutions yield the x-intercepts as (2,0) and (-3,0), so we have enough information.

Note: Since there are two x-intercepts, the question should have read "at what points does y = (x + a)(x + b) cross the x axis?"

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