Please help if possible, C2.

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.

Reply 1

AndroidLight

18

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).

Reply 2

petoid12

5

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 :smile:

thennn, you can use the discriminant to find and expression for k... I think.

2. Just use your calc to plot the graph :s

Reply 3

EzPz

OP

6

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!

Reply 4

Dirac Spinor

10

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

Reply 5

EzPz

OP

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 :smile:

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.

Reply 6

EzPz

OP

6

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!

Reply 7

AndroidLight

18

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!