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Source: — Data Sufficiency |
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by mathbyvemuri » Fri May 11, 2012 7:17 pm
y = (x+a)(x+b)
To find the points of intersection with X-axis, substitute y=0,which is the equation of X-axis, in the given equation.
(x+a)(x+b)=0
x = -a or -b.
So, (-a,0) and (-b,0) are the points of intersection on X-axis. (as y-coordinates are obviously zero)
So, the problem is to find a and b values.
statement(1)=> gives only one equation in a and b and hence not sufficient to get a and b
statement(2)=>point of intersection on Y-axis is given (0,-6)
To find the points of intersection on Y-axis, substitute x=0,which is the equation of Y-axis, in the given equation.
y = ab
but the point of intersection is given as (0,-6) => y = -6 = ab
=> this gives a new relation between a and b, which when taken together with statement(1),resolves values of a and b
Answer"C"
Last edited by mathbyvemuri on Fri May 11, 2012 7:44 pm, edited 1 time in total.
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by Anurag@Gurome » Fri May 11, 2012 7:42 pm
myfish 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)
Given: y = (x + a)(x + b)
Implies the graph intersects x-axis at x = -a or x = -b.
Thus we have to find the values of a and b.

Statement 1: (a + b) = -1
Infinite numbers of values are possible for a and b.

Not sufficient.

Statement 2: The graph intersects y-axis at (0, -6)
For x = 0, y = (0 + a)(0 + b) = ab = -6
Infinite numbers of values are possible for a and b.

Not sufficient.

1 and 2 Together: (a + b) = -1 and ab = -6
Now, (a - b)² = (a + b)² - 4ab = (-1)² - 4*(-6) = 25
=> (a - b) = ±5

Thus, either (a = 2, b = -3) or (a = -3, b = 2)
In both of the cases the graph intersects x-axis at x = -3 and x = 2.

Sufficient.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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