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    I just need to check something; when you multiply out (2√x + 3)² do you get 4x + 4√x + 9 ?

    I also am a bit comfused at this question:

    Solve the equation 4x² + 12x=0

    f(x)=4x² + 12x + c
    where c is a constant

    b) Given that f(x) = 0 has equal roots, find the value of c and hence solve f(x)=0

    Thanks in advance.
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    No, you get 4x + 12√x + 9

    4x² + 12x=0
    x(4x+12)=0
    x=0,-3

    b^2-4ac = 0
    4ac = b^2
    c = b^2/4a

    f(x)=4x² + 12x + 12^2/4*4
    =4x^2 + 12x + 9
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    a) Factorise! 4x(x+3) = 0 - Can you see what to do from there?

    b) if there are two equal roots the equation can be written as (2x - a)^2 = 0. Multiply this out and equate coefficients to get the value of a and hence c
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    (Original post by mik1a)
    No, you get 4x + 12√x + 9
    No, you get 4x + 6√x + 9.

    Ben

    EDIT [Oh, I see - I thought he was just stipulating a square root with the 2, sorry]
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    (2√x + 3)² = 4x + 12√x + 9


    4x² + 12x=0
    4x(x+3) =0
    x= 0,-3


    4x² + 12x + c =0
    (2x + 3)(2x + 3) = 0
    c=9
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    (Original post by Ben.S.)
    No, you get 4x + 6√x + 9.

    Ben
    No, you get 4x + 12√x + 9
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    (Original post by Zapsta)
    No, you get 4x + 12√x + 9
    Not if you read it as it's written!

    Ben
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    Firstly, (2sqrt(x) + 3)^2 = 4x + 12sqrt(x) + 9.

    To solve 4x^2 + 12x=0 factorise out 4x to give 4x(x+3)=0 so the solutions are x=0 or -3.

    If f(x) has equal roots, the discriminant is equal to zero. That is, b^2-4ac=0. We have a=4, b=12 and we want to find c. Therefore, 144 - 4(4)c=0 => c=144/16 = 9. Thus, f(x) = 4x^2 + 12x + 9 = (2x+3)^2 so the root is -3/2.

    I hope this helps.
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    (Original post by Ben.S.)
    Not if you read it as it's written!

    Ben
    Ah yeah, sorry the fonts on my computer change when I use symbols from the character map. I actually meant to write 4x + 12√x + 9 I can't think why I wrote 4x + 4√x + 9 instead.

    Thanks everyone.
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    Hehe I beat you all to it
 
 
 

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