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    https://917c8db4f385e20466384eff57d8...%20Edexcel.pdf

    Question 7c how do you show this?
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    (Original post by Acrux)
    https://917c8db4f385e20466384eff57d8...%20Edexcel.pdf

    Question 7c how do you show this?
    What have you tried so far?
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    (Original post by SeanFM)
    What have you tried so far?
    solving for k but this gets you no where
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    Discriminant: (k+3)^2-4k = k^2+2k+9 = (k+1)^2+8

    Real roots if discriminant ≥0: Clearly (k+1)^2+8\geq0 since minimum point is (-1,8) (i.e it lies above the x-axis so is positive)
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     f(x) will have real roots if the discriminant is greater, or equal to 0 (question does not say roots have to be distinct).
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    (Original post by Math12345)
    Discriminant: (k+3)^2-4k = k^2+2k+9 = (k+1)^2+8

    Real roots if discriminant ≥0: Clearly (k+1)^2+8\geq0 since minimum point is (-1,8)
    Well done but would it not be more beneficial to the OP if you questioned them, instead of giving the answer?
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    You have to calculate the discriminant.
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    (Original post by Acrux)
    solving for k but this gets you no where
    With questions with multiple parts, most of the time there is a link at some point.

    You've found an expression for the discriminant, and you know that when f(x) = 0 and the equation has real roots, the discriminant is...

    So the link is..
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    (Original post by The-Spartan)
    Well done but would it not be more beneficial to the OP if you questioned them, instead of giving the answer?
    Sorry boss
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    (Original post by Math12345)
    Discriminant: (k+3)^2-4k = k^2+2k+9 = (k+1)^2+8

    Real roots if discriminant ≥0: Clearly (k+1)^2+8\geq0 since minimum point is (-1,8) (i.e it lies above the x-axis so is positive)
    what does the minimum point imply
    so what is positive..?
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    (Original post by Acrux)
    what does the minimum point imply
    so what is positive..?
    For f(x)=0 to have real roots, the discriminant must be greater than or equal to 0. Clearly the discriminant (k+1)^2+8 is greater or equal to 0 (sketch it) - I just said the minimum point is (-1,8) to show that the discriminant is ≥0. You could just say (k+1)^2≥0 for the mark (the square of real numbers is positive).
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    (Original post by Math12345)
    For f(x)=0 to have real roots, the discriminant must be greater than or equal to 0. Clearly the discriminant (k+1)^2+8 is greater or equal to 0 (sketch it) - I just said the minimum point is (-1,8) to show that the discriminant is ≥0. You could just say (k+1)^2≥0 for the mark (the square of real numbers is positive).
    However if the discriminant is greater than zero shouldnt there be roots this graph does not cross the x-axis
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    (Original post by SeanFM)
    With questions with multiple parts, most of the time there is a link at some point.

    You've found an expression for the discriminant, and you know that when f(x) = 0 and the equation has real roots, the discriminant is...

    So the link is..
    How do you workout 9bi?
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    (Original post by Acrux)
    However if the discriminant is greater than zero shouldnt there be roots this graph does not cross the x-axis
    No, you are missing the point. f(x) will cross the x-axis and have roots!, but the discriminant is completely different. We need to show that the discriminant is positive (i.e is always above the x-axis) to show that f(x) has real roots
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    (Original post by Acrux)
    How do you workout 9bi?
    What have you tried so far?
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    (Original post by Math12345)
    No, you are missing the point. f(x) will cross the x-axis and have roots!, but the discriminant is completely different. We need to show that the discriminant is positive (i.e is always above the x-axis) to show that f(x) has real roots
    Ok i understand now
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    (Original post by SeanFM)
    What have you tried so far?
    Un=k+(100-1)k
    =100k
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    k+2k+3k+....+100=k(1+2+3+...+ \frac{100}{k})

    How many terms?
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    (Original post by Math12345)
    k+2k+3k+....+100=k(1+2+...100/k)

    How many terms?
    100 terms
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    (Original post by Acrux)
    100 terms
    Careful.

    Count the bits in the brackets (1,2.....)
 
 
 
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