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    Find the values of k for which the equation x^2 - kx + (k+3) = 0 has real roots.

    How would I go about doing this? Help would be much appreciated.
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    What is b^2 - 4ac (the discriminant) equal to when an equation has real roots?
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    you know the discriminant must be greater than zero.

    D = b^2-4ac
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    real roots so b^2-4ac>0. So k^2-4(1)(k+3)>0. Just solve the inequality ( you do know how to, right?).

    EDIT: if an equation has real roots, then b^2-4ac>0. If an equation has equal roots, then b^2-4ac=0. If an equation has no real roots, then b^2-4ac<0
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    :facepalm:

    Of course. K is less than or equal to 2 and greater than or equal to 6. Thank you all

    Edit: -2 not 2
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    (Original post by mya369)
    :facepalm:

    Of course. K is less than or equal to 2 and greater than or equal to 6. Thank you all
    Incorrect. It is less than 2 and greater than 6. By putting -2 in, you get:  x^2-2x+1. For that equation, b^2-4ac=0 - so it has to be less than -2. If you put 6 into the equation, then it will be: x^2+6x+9. b^2-4ac is equal to zero again. It is better to draw a curve going through both points and then look at the part above the x axis for >0 or the part below the x axis for <0.
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    (Original post by mya369)
    :facepalm:

    Of course. K is less than or equal to 2 and greater than or equal to 6. Thank you all
    actually i think it's -6 and 2

    EDIT: i was wrong, I miss-read your post sorry
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    (Original post by MostCompetitive)
    Incorrect. It is less than 2 and greater than 6. By putting -2 in, you get:  x^2-2x+1. For that equation, b^2-4ac=0 - so it has to be less than -2. If you put 6 into the equation, then it will be: x^2+6x+9. b^2-4ac is equal to zero again. It is always easier to draw a curve going through both points then looking at the part above the x axis for >0 or the part below the x axis for <0.
    pretty sure "real roots" includes the situation of a repeated root. if it said "distinct roots", i'd agree with you
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    (Original post by MostCompetitive)
    Incorrect. It is less than 2 and greater than 6. By putting -2 in, you get:  x^2-2x+1. For that equation, b^2-4ac=0 - so it has to be less than -2. If you put 6 into the equation, then it will be: x^2+6x+9. b^2-4ac is equal to zero again. It is better to draw a curve going through both points and then look at the part above the x axis for >0 or the part below the x axis for <0.
    I think that 2 and 6 are inclusive. Repeated roots are still real roots.
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    (Original post by MostCompetitive)
    Incorrect. It is less than 2 and greater than 6. By putting -2 in, you get:  x^2-2x+1. For that equation, b^2-4ac=0 - so it has to be less than -2. If you put 6 into the equation, then it will be: x^2+6x+9. b^2-4ac is equal to zero again. It is better to draw a curve going through both points and then look at the part above the x axis for >0 or the part below the x axis for <0.
    Gunna go with equal roots being included. Thanks though
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    (Original post by Pheylan)
    pretty sure "real roots" includes the situation of a repeated root. if it said "distinct roots", i'd agree with you
    It doesn't. That is because when an equation has real roots, b^2-4ac&gt;0. That doesn't include equal to zero.
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    (Original post by mya369)
    Gunna go with equal roots being included. Thanks though
    > than 0 doesn't include equal to 0. Because i've done this paper recently, I can show you the mark scheme if you want.
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    (Original post by MostCompetitive)
    > than 0 doesn't include equal to 0. Because i've done this paper recently, I can show you the mark scheme if you want.
    I'm sure you can, but I found this question in an edexcel textbook. Their answer and the answers to similar questions include equal roots.

    I agree with you in that if they state that for real roots the discriminant is greater than 0 (which they do), but not greater than or equal to 0, they shouldn't include equal roots in their answer. They aren't being consistent.
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    (Original post by mya369)
    . They aren't being consistent.
    I agree
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    The answer is just,

    it forms equal roots when k is 6, or when k is -2. There is no "less than.." or "greater than.." involved.

    E.g when k = 6, it forms x^2 - 6x + 9 = (x - 3)(x - 3)
 
 
 
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