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 point
s does y = (x + a)(x + b) cross the x axis?"
