data sufficiency

[Kim9876Zey]

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)

correct answer is both statement together

I am having a hard time placing y=(x+a)(x+b) with option one

[Jim@StratusPrep]

From the statement, we know that the parabola crosses the x-axis when x=a or when x=b, because y will then equal 0.

1) a and b can be anything.
2) we know that a or b = 6

Together, we know that the two possible values for a and b are 6 and -5. It doesn't matter which is which, because we know the two points. The two points are then (0,-6) and (0,5).

[jcnasia]

y = (x + a)(x + b)
y = x^2 + ax + bx + ab
y = x^2 + (a+b)x + ab

The prompt tells us that it crosses y-axis at (0,-6), therefore:
-6 = 0^2 + 0 + ab
-6 = ab

And, to figure out when this equation crosses the x-axis, we set y = 0, and solve the equation:
0 = (x+a)(x+b)
x = -a or -b

So in order to figure out what a and b are equal to, I need to find two numbers that add up to 1 (since a + b = 1) and multiply together to get -6 (since ab = -6). I can do this in my head. I hope you can do.

(This is my mind thinking...)
Since they multiply together to get -6, I know that one is positive and and one is negative.
Since they add up to 1 and one is negative and one is positive, I know that their respective absolute values have a difference of 1. And since, they add up to 1 and not -1, I know that the absolute value of the positive number is bigger than the absolute value of the negative number.

So, what two numbers multiply together to get 6? And have a difference of 1?
3 and 2!

So 3 and 2 are the absolute values of a and b.

And since they need to add up to 1, then a and b are 3 and -2

Thus, x = -3 or 2 (since x = -a or -b)
The intersection points are (-3,0) and (2,0).

[jcnasia]

From the statement, we know that the parabola crosses the x-axis when x=a or when x=b, because y will then equal 0.

1) a and b can be anything.
2) we know that a or b = 6

Together, we know that the two possible values for a and b are 6 and -5. It doesn't matter which is which, because we know the two points. The two points are then (0,-6) and (0,5).

This is incorrect.
First of all, x = -a or x = -b when y = 0.
Second, a and b can't be anything. They have to add up to 1 and multiply together to get -6.
Third, neither a nor b = 6.
Fourth, (0,-6) and (0,5) aren't even on the x-axis. They're on the y-axis.