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25 Nov 2007, 20:23
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In the xy-plane at what points does the graph of y =(x+a)(x+b) intersect the x-axis?
(1). a + b = -1
(2). The graph intersect the yaxis ast (0,-6)
Solution :
Wait for you solution. thanks
(1). a + b = -1
(2). The graph intersect the yaxis ast (0,-6)
Solution :
Wait for you solution. thanks
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25 Nov 2007, 23:20
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C
y =(x+a)(x+b) - parabola that intersect x-axis at points (-a,0) and (-b,0)
Therefore, we should known both a and b.
1. a + b = -1 (-3,2) and (-2,1) match equation - insufficient
2. The graph intersect the yaxis ast (0,-6) means -6=(0+a)(0+b) ==> ab=-6
(-3,2) and (1,-6) match equation - insufficient
1&2. a + b = -1 and ab=-6 ==> solution: -3 and 2 sufficient
y =(x+a)(x+b) - parabola that intersect x-axis at points (-a,0) and (-b,0)
Therefore, we should known both a and b.
1. a + b = -1 (-3,2) and (-2,1) match equation - insufficient
2. The graph intersect the yaxis ast (0,-6) means -6=(0+a)(0+b) ==> ab=-6
(-3,2) and (1,-6) match equation - insufficient
1&2. a + b = -1 and ab=-6 ==> solution: -3 and 2 sufficient
26 Nov 2007, 00:08
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also for C,
1) INSUFF
a+b=-1-------------> (a,b) could be 0,-1 ; -5,4 ; or vice versa
2) INSUFF
ab=-6--------------> (a,b) could be 1,-6 ; -2;3 ; or vice versa
both) SUFF
a= -1-b
ab= (-1-b)b
b^2-b-6=0
b=2 or b=-3
b=2 a= -3
b=-3 a=2
in any case parabola intersects x axis at (3,0) and (-2,0)
1) INSUFF
a+b=-1-------------> (a,b) could be 0,-1 ; -5,4 ; or vice versa
2) INSUFF
ab=-6--------------> (a,b) could be 1,-6 ; -2;3 ; or vice versa
both) SUFF
a= -1-b
ab= (-1-b)b
b^2-b-6=0
b=2 or b=-3
b=2 a= -3
b=-3 a=2
in any case parabola intersects x axis at (3,0) and (-2,0)
