coordinate geometry

[smohsin]

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)

Thanks

[uttara]

its a variation of the question in the below link.

https://www.beatthegmat.com/mgmatds4-t21109.html

[smohsin]

i tried solving the equation with statements 1 and 2, but i get two values for x, as I had solved for a quadratic equation. i got x=6 and x=7. is that right?

can you please show the work behind the problem?

[uttara]

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)

--------

y = (x+a)(x+b)
expanding it, u get
y= x^2+(a+b)x+(ab) ----- (A)

from option(1) we get value of only a+b. we still need ab, hence it alone is insufficient.

from option(2)
by putting x=0 & y=-6 in equation (A), we get
-6=0+0+ab
ie ab= -6

by using both options together in (A), we get
y=x^2 -1x -6
this line will intersect the x-axis at a point where y=0
ie
0=x^2 -1x -6
x^2 -3x +2x -6 = 0
(x-3)(x+2)=0
ie x=3 or x=-2

note that we are asked to find
In the xy plane at what two points does the graph of y = (x+a)(x+b) intersect the x-axis.

Hence the two points are (3,0) & (-2,0)

So (C) is the correct answer

[smohsin]

Thanks SO much!

[venmic]

The way to slve the prblem is given
BUT
what is the concept here
can anyone help please
as in on what basis would this question have been solved

what should we have been looking here for

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)

Thanks