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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.
2. 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).
3. 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
4. (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!
5. 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
6. (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.
7. (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
Yeah the discriminant one doesn't seem to work??? Or perhaps im doing something wrong.

Got the transformation one now thanks!
8. (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
9. Where are you getting these questions from? Did you copy no.one correctly?
10. (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!
11. (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.
12. 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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