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13 Sep 2005, 18:32
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N
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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 intersects y axis at (0,-6)
1. a+b =-1
2. The graph intersects y axis at (0,-6)
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13 Sep 2005, 19:54
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I will go with C.
y = (x + a) (x+b)
or
y = x^2 + (a+b)x + ab .....(a)
in order to cut x axis, y = 0. OR
x ^ 2 + (a + b) x + ab = 0
i) insufficient
ii) putting (0, -6) into equation (a) gives
ab = -6
taking both these,
cuts x axis when:
x^2 - x - 6 = 0
or x = 3, -2
As question asking "Points", having more than one anser is ok.
y = (x + a) (x+b)
or
y = x^2 + (a+b)x + ab .....(a)
in order to cut x axis, y = 0. OR
x ^ 2 + (a + b) x + ab = 0
i) insufficient
ii) putting (0, -6) into equation (a) gives
ab = -6
taking both these,
cuts x axis when:
x^2 - x - 6 = 0
or x = 3, -2
As question asking "Points", having more than one anser is ok.
13 Sep 2005, 20:01
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C
At one point the the graph cuts x-axis. Equation of x-axis is y=0
Substituting... we can simplify the function to
(X+a)(X+b)
or essentially what is (-a,-b) ?... or what are the values of a & b?
i) a+b = -1 Insuff
ii) Graph intersects Y axis - so x=0, y=-6 .. replace in the parent equation to get value of ab = -6 .. insuff
from i) & ii) we have 2 equations... solve for a & b... Together they are suff => C.
At one point the the graph cuts x-axis. Equation of x-axis is y=0
Substituting... we can simplify the function to
(X+a)(X+b)
or essentially what is (-a,-b) ?... or what are the values of a & b?
i) a+b = -1 Insuff
ii) Graph intersects Y axis - so x=0, y=-6 .. replace in the parent equation to get value of ab = -6 .. insuff
from i) & ii) we have 2 equations... solve for a & b... Together they are suff => C.
