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C1 maths coordinate question?

I am stuck on part c of this question. Can you please help me?? A step by step explanation would be useful!

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if you have

x(a quadratic in x) = 0

then either x = 0 or the quadratic = 0

since they want surds in the answer it is not likely that the quadratic will factorise.
Reply 2
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ayylmao97
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Original post by the bear
if you have

x(a quadratic in x) = 0

then either x = 0 or the quadratic = 0

since they want surds in the answer it is not likely that the quadratic will factorise.

how am i supposed to find the coordinates?
You need to start by finding the roots of the equation x(x^2-8x+4). This can be found by using the quadratic formula on the inside part of the bracket. This will then give you three answers: 0 (because of the x outside of the brackets) and two surds. The positive one is the x-coordinate.

Next, you need to put the x-coordinate into one of the original formulae in order to work out the y-coordinate.

Hope this helps!
Original post by ayylmao97
how am i supposed to find the coordinates?


you get the x coordinates by solving the equation, then to find the y coordinates you put the x coordinates into one of the two original functions ( it does not matter which ).
Did you get the answer?
Reply 6
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ayylmao97
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Original post by Student 977
Did you get the answer?

no, i don't know how to solve the equation
Original post by ayylmao97
no, i don't know how to solve the equation


You need to use the quadratic formula on (x^2-8x+4). This will give you two answers as surds. Can you do that?
Reply 8
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ayylmao97
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Original post by Student 977
You need to use the quadratic formula on (x^2-8x+4). This will give you two answers as surds. Can you do that?

so far i got to (8+-√48)/2 but i don't know how to cancel down the root
Original post by ayylmao97
so far i got to (8+-√48)/2 but i don't know how to cancel down the root


I forgot it was a non-calculator paper! You need to complete the square of x^2-8x+4.
Maths.jpg

Here is some help!
Reply 11
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ayylmao97
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Original post by Student 977
I forgot it was a non-calculator paper! You need to complete the square of x^2-8x+4.


I've done it, and I got (x-4)^2-12
Original post by ayylmao97
I've done it, and I got (x-4)^2-12


Yes and then you can equate that to x
Reply 13
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ayylmao97
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Original post by Student 977
Yes and then you can equate that to x


After that do I substitute the x coordinate into one of the equations to find y?
Original post by ayylmao97
After that do I substitute the x coordinate into one of the equations to find y?


Yes, but make sure you use the correct x-coordinate.
Reply 15
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ayylmao97
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Original post by Student 977
Yes, but make sure you use the correct x-coordinate.


Lool sorry to keep bothering you like this but I don't know how to expand the brackets once I've substituted x
Which equation did you put the x into?
Reply 17
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ayylmao97
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Original post by Student 977
Which equation did you put the x into?


Into the x(4-x)
So you get (4-2rt3)(4-4-2rt3)
Reply 19
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ayylmao97
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Original post by Student 977
So you get (4-2rt3)(4-4-2rt3)

yes but then wouldnt the second bracket cancel down to (4-2rt3)?

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