In the x-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 - axix at (0 , -6) As usual, OA after some discussion

Intersecting the X-axis means that y = 0. This is accomplished when x is either -a or -b. So in order to solve this problem, you need to know a and b. y will also be x^2 + (a +b)x + ab. 1. a + b = -1 is not enough to find a and b, so this one is insufficient 2. this tells us that point (0, -6) is on the graph or that -6 = ab. Again, this is not enough to solve for a and b, since you have two unknowns and only one equation. But put the two together and you can solve the problem. Notice that -6 is -3*2, which will be a and b (since it is consistent with a + b = -1), so we have solved the problem. I'd go with C. EDIT: Thank you, missed that.

DanaJ wrote:Intersecting the X-axis means that y = 0. This is accomplished when x is either -a or -b. So in order to solve this problem, you need to know a and b. y will also be x^2 + (a +b)x + ab. 1. a + b = -1 is not enough to find a and b, so this one is insufficient 2. this tells us that point (0, -6) is on the graph or that 0 = 36 - 6(a + b) + ab. Again, this is not enough to solve for a and b, since you have two unknowns and only one equation. But put the two together and you get that 0 = 36 + 6 + ab or that ab = - 42. Notice that -42 is -7*6, which will be a and b (since it is consistent with a + b = -1), so we have solved the problem. I'd go with C. I will agree with the approach. But solutioning(which obviously is not needed is little incorrect) 2. this tells us that point (0, -6) is on the graph or that x = 0 and y = -6 ==> solving for x and y, we get ab = -6. Again, this is not enough to solve for a and b, since you have two unknowns and only one equation. But putting together we have, a+b = -1 and ab = -6. Two distinct eqs and two unknowns. So we should be able to get solve for X intercepts. I will go with C.