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Core 1 Further equations

the straight line L has the equation y=3x-1 and the curve C has equation y=(x+3)(x-1)

a) sketch on the same axes the line L and the curve C showing the values of the intercepts on the x-axes and the y axes

b)show that the x-coordinates of the points of interception of L and C satisfy the equation x^2-x-2=0

c)hence find the coordinates of the points of interception of L and C


I have done question a but I really am lost with question b as in class we haven't really done much on this and in the textbook and revision guide I can not seem to find anything explaining it. any help appreciated
Reply 1
Avatar for Notnek
Notnek
21
Original post by βradley
the straight line L has the equation y=3x-1 and the curve C has equation y=(x+3)(x-1)

a) sketch on the same axes the line L and the curve C showing the values of the intercepts on the x-axes and the y axes

b)show that the x-coordinates of the points of interception of L and C satisfy the equation x^2-x-2=0

c)hence find the coordinates of the points of interception of L and C


I have done question a but I really am lost with question b as in class we haven't really done much on this and in the textbook and revision guide I can not seem to find anything explaining it. any help appreciated

If the question was, "Find the coordinates of intersection of L and C", would you be able to do it? How do you find the intersection of two lines/curves given their equations?

Your question is basically the same, just in your working you should arrive at x^2-x-2=0.

Post all your working/thoughts if you get stuck.
Original post by βradley
the straight line L has the equation y=3x-1 and the curve C has equation y=(x+3)(x-1)

a) sketch on the same axes the line L and the curve C showing the values of the intercepts on the x-axes and the y axes

b)show that the x-coordinates of the points of interception of L and C satisfy the equation x^2-x-2=0

c)hence find the coordinates of the points of interception of L and C


I have done question a but I really am lost with question b as in class we haven't really done much on this and in the textbook and revision guide I can not seem to find anything explaining it. any help appreciated


At intersections, the coordinates are the same. Since the y-coordinates are the same, you can equate them to each other and simplify.
Where they intercept, they must be equal to each other. Therefore you can set 3x-1 = (x+3)(x-1)
Now try and manipulate that and see if you get the equation given in the question
Reply 4
Avatar for Pangol
Pangol
15
The y coordinate of the points of intersection will be 3x-1 (because the points are on the line) AND (x+3)(x-1) because the points are on the curve). So, put those two expressions equal to each other, and see if you can end up with the equation they have given you.
Reply 5
Avatar for βradley
βradley
OP
2
IMG_3003.jpg
This is what i have finished with. Thanks for the help let me know if anything isn't right

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