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    Find the two points on the curve Y=2x^3 - 5x^2 +9x -1 where the gradient = 13.

    So i differentaited to get 6x^2 -10x +9 I then set that equal to the gradient so 6x^2 -10x +9 =13. Then I turned it into a quadratic by subtracting to get 6x^2 -10x +9 =0 and was going to solve for x that way but its a non calculatro question and the asnweres in thebook are given as a fraction, ut i cant see how to factorise this anyone help?
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    Use the quadratic formula?
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    PS Reviewer
    Complete the square :yep:
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    (Original post by -beads-)
    Use the quadratic formula?
    I did intally but doing all those surds and things without a claultor makes it very difficult =/
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    Is it not: 6x^2 - 10x - 4 = 0 (have to subtract the thirteen)

    That becomes 3x^2 - 5x - 2 = 0 (dividing by 2)

    This can be factorised.
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    (Original post by cpdavis)
    Complete the square :yep:
    Forogt how to do it . I remeber you half the coefficent of b so i would get -5 and you square it all or something
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    (Original post by jaheen22)
    Is it not: 6x^2 - 10x - 4 = 0 (have to subtract the thirteen)

    That becomes 3x^2 - 5x - 2 = 0 (dividing by 2)

    This can be factorised.
    :O maybe although im bad at factosriisng it takes me ages =/
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    (Original post by hazbaz)
    :O maybe although im bad at factosriisng it takes me ages =/
    You need two numbers that multiply together to get -2 and when is one multiplied by 3 they add to give -5.

    ANS:
    Spoiler:
    Show
    (3x+1)(x-2)
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    A similar question was posted like this couple of days ago. Why start a new thread on this?
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    6x^2 -10x +9 =13
    6x^2-10x-4=0
    3x^2-5x-2=0
    (3x+1)(x-2)=0
    =]
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    Factorised it to get (-3x -1) (-x +2) so x = 1 or x = -2 so i subsititued these into the y = equation to get y = 5 or y = -39 so the points would be (1,5) or (-2, -39) but in the book it says the answer is (-1/3, -4 17/27) and (2,13)
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    x = 2 and x = -1/3, the x values you got are wrong!
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    (Original post by hazbaz)
    I did intally but doing all those surds and things without a claultor makes it very difficult =/
    You're doing it wrong. :ahee:

    But if you were to obtain an answer in surd form... that's perfectly fine to leave it like that in the exam.

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    (Original post by boromir9111)
    x = 2 and x = -1/3, the x values you got are wrong!
    Opp ye it should be (3x +1) (x -2) I understand why x = 2 but not 1/3 woudnt it just be -1 beucase you swap the sign of the +1 ?
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    (Original post by hazbaz)
    Opp ye it should be (3x +1) (x -2) I understand why x = 2 but not 1/3 woudnt it just be -1 beucase you swap the sign of the +1 ?
    3x+1 = 0
    3x = -1
    x = -1/3

    If you didn't understand that, don't be shy to post here
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    (Original post by boromir9111)
    3x+1 = 0
    3x = -1
    x = -1/3

    If you didn't understand that, don't be shy to post here
    Ah right ye that makes sense and then i just plug those 2 values in to get Y?
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    (Original post by hazbaz)
    Ah right ye that makes sense and then i just plug those 2 values in to get Y?
    :yes:
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    They alos get an asnwer of (2,13)...
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    (Original post by hazbaz)
    They alos get an asnwer of (2,13)...
    Sub x =2 into the original function and that will give y which is 13 Do you understand how that is done?
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    (Original post by hazbaz)
    Find the two points on the curve Y=2x^3 - 5x^2 +9x -1 where the gradient = 13.

    So i differentaited to get 6x^2 -10x +9 I then set that equal to the gradient so 6x^2 -10x +9 =13. Then I turned it into a quadratic by subtracting to get 6x^2 -10x +9 =0 and was going to solve for x that way but its a non calculatro question and the asnweres in thebook are given as a fraction, ut i cant see how to factorise this anyone help?
    Is this a typo or did you forget to subtract 13 from both sides?

    Last equation should read 6x^2 - 10x - 4 = 0
    => 6x^2 - 12x + 2x - 4 = 0
    => 6x(x - 2) + 2(x - 2) = 0
    => (6x + 2)(x - 2) = 0

    .: x = 2 or x = -1/3

    EDIT:

    Oh already been answered. And yea I should have divided through by two but this illustrates the method where you split up the bx term and then factorise it in stages. Which I always found easier lol.
 
 
 
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