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    Thanks for reading,

    1) (5-kx)(x+4) = 0 has no real roots, find an expression in terms of k for this equation.


    2) Sketch the graphs of y=-tan(0.5x) between 0<x<360


    If anyone can help it would be much appreciated.
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    2) Draw the graph of tan(x). Then apply the transformations. Do you know how the minus and the 0.5x would affect the graph?

    1) I think what you do is multiply out and use that if there's no real roots, in the quadratic formula, the part b squared minus 4ac (the discriminant) is less than 0 (as b squared minus 4ac is square rooted, and if it is less than 0 then there will not be any roots).
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    I haven't done this in a while... but...

    1. I think that if you were to expand the brackets then you will have a quadratic thennn, you can use the discriminant to find and expression for k... I think.

    2. Just use your calc to plot the graph :s
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    (Original post by AndroidLight)
    2) Draw the graph of tan(x). Then apply the transformations. Do you know how the minus and the 0.5x would affect the graph?

    1) I think what you do is multiply out and use that if there's no real roots, in the quadratic formula, the part b squared minus 4ac (the discriminant) is less than 0 (as b squared minus 4ac is square rooted, and if it is less than 0 then there will not be any roots).
    Thanks for the reply, the minus will cause a reflection in the x-axis, then the 0.5 I thought would stretch by SF 2?

    For the discriminant question, i multiply out the brackets to get..
    5x+20-kx^2-4kx < 0
    I got confused here as to how you can use b^2-4ac with 4 integers/constants.

    Thanks again!
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    I'm slightly puzzled as to one. It does have at least one real root at x=-4.
    2 is just routine transformations. It is a stretch in the x direction factor 2 followed by a reflection in the x axis of a y=tanx graph
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    (Original post by petoid12)
    I haven't done this in a while... but...

    1. I think that if you were to expand the brackets then you will have a quadratic thennn, you can use the discriminant to find and expression for k... I think.

    2. Just use your calc to plot the graph :s
    Thanks for the response. Good shout with 'using the calc' - Do want to understand why though.

    The discriminant question i'm stuck on after expanding the brackets.
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    (Original post by ben-smith)
    I'm slightly puzzled as to one. It does have at least one real root at x=-4.
    2 is just routine transformations. It is a stretch in the x direction factor 2 followed by a reflection in the x axis of a y=tanx graph
    Thanks for the reply.
    Yeah the discriminant one doesn't seem to work??? Or perhaps im doing something wrong.

    Got the transformation one now thanks!
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    (Original post by EzPz)
    Thanks for the reply, the minus will cause a reflection in the x-axis, then the 0.5 I thought would stretch by SF 2?

    For the discriminant question, i multiply out the brackets to get..
    5x+20-kx^2-4kx < 0
    I got confused here as to how you can use b^2-4ac with 4 integers/constants.

    Thanks again!
    - kx^2 - (4kx+5x) + 20

    so b^2 - 4ac
    (4k+5)^2 - 4(-k+20) <0

    Or something like that, bit rushed, sorry, hopefully you follow what's going on
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    Where are you getting these questions from? Did you copy no.one correctly?
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    (Original post by AndroidLight)
    - kx^2 - (4kx+5x) + 20

    so b^2 - 4ac
    (4k+5)^2 - 4(-k+20) <0

    Or something like that, bit rushed, sorry, hopefully you follow what's going on
    Really appreciate the help here, thanks so much!
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    (Original post by ben-smith)
    Where are you getting these questions from? Did you copy no.one correctly?
    Yeah it's copied correctly, its a homework question.

    Can't seem to work out why it is what 'android light' said.
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    Well tell your teacher that you could not answer the question as it has an internal contradiction. i.e excuse to not do it lol
 
 
 
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