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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)
Can somebody show me how to solve this? thanks
The line intesects the x axis when y is zero. The problem is that you have to many variables.
Stmt 1 alone reduces the number of variables from 4 to 3 and is not suff.
Stmt 2 alone reduces the number of variales from 4 to 2 and is not suff.
Together you can use stmt 1 to write the equation in terms of y,x,b. You can then use stmt 2 to plug in y and x and get b. You then have the equation of the line and can find where it intersects the x axis.
y = (x + a) (x + b)
from the question, we need intercept of x, so y = 0
(x + a) (x + b) = 0
x = -a or -b
1) a+b = -1
2) lines intersects y-axis at (0,6)
so -6 =(0+a) (0+b)
ab = -6
buy solving one and two you can have x = 3, -2.
So we have two points and so I think ans is E or C???.
Pls let us know the OA.
guys, the OA to this is C. So we need to figure out how exactly is it so. would anyone please explain?
I could try
With y=(x+a)*(x+b), the intersection with X axis is obtained by using the equation of the x axis.
The X axis has y=0 for equation.
So, now, we have the following system:
o y=(x+a)*(x+b)
o y=0
That means:
(x+a)*(x+b) = 0
Before going further and keeping a concrete view of we talk about, I would like to bring your attention on y=(x+a)*(x+b). It's the equation of parabola such that y = u*x^2 + v*x + w where u = 1, making it in the shape of a valley in the XY plane.
Having said that, we have 2 cases to make (x+a)*(x+b) = 0:
> x = -a
or
> x = -b
So, we know that the 2 points are at (-a,0) and (-b,0).
All we have to do now is to look if we can have values for a and for b.
(C) it is ... We have to solve a symetrical system, from which a and b can be interverted yet we can know the 2 points (a and b are not the final things we are asked to know) :
o a+b = -1
and
o a*b = -6
guys, i understand why A and B aren't suff., however, i'm still confused with how option C is suff. can somebody show me the exact steps of the calculation in order to make option C suff?
guys, i understand why A and B aren't suff., however, i'm still confused with how option C is suff. can somebody show me the exact steps of the calculation in order to make option C suff?
(x+a)*(x+b)
= x^2 + (a+b)*x + a*b
Stat 1.... Give us a+b = -1
Stat 2... If x = 0, then y = -6....
So, y = -6 = x^2 + (a+b)*x + a*b = 0^2 + (a+b)*0 + a*b
<=> a*b = -6
Stat 1 & 2 o a + b = -1
o a*b = -6
U can solve it by replacing a or b in a*b = -6... But in the G day, u better not do so
U have 2 different equations with 2 unknown variables... and a symetrical system here from which we could not define what is a or b in certitude. Again, that's not relevant to conclude
Let me develop it anyway
o b = -1 - a = -(a+1)
o a*b = a*(-1*(a+1)) = -6
<=> -a*(a+1) = -6
<=> a^2 + a = 6
<=> a^2 + a - 6 = 0