Decimal Search Failure: is this function allowed?

I need to show a function where the decimal search method doesn't work for it, for example, one with a repeated root.
I initially chose this:

f(x) = (2x-\pi)^3 - (2x-\pi)^2

But I can easily tell that that

f(\frac{\pi}{2})=0

so can I use this if I actually know the root and can represent it precisely?

Reply 1

ghostwalker

Original post by Primus2x

I need to show a function where the decimal search method doesn't work for it, for example, one with a repeated root.
I initially chose this:

f(x) = (2x-\pi)^3 - (2x-\pi)^2

But I can easily tell that that

f(\frac{\pi}{2})=0

so can I use this if I actually know the root and can represent it precisely?

Seems fine to me.

You could go for something a bit more esoteric, such as (cos(x)-x)^2, then even knowing that the root is the solution to cos(x)=x, you still can't work it out analytically, and have to use numerical methods.

Reply 2

Primus2x

Original post by ghostwalker

So any function is allowed, as long as it doesn't have integer roots? It doesn't matter if I can factorise it and/or know the root precisely?

Reply 3

ghostwalker

Original post by Primus2x

So any function is allowed, as long as it doesn't have integer roots? It doesn't matter if I can factorise it and/or know the root precisely?

From what you've posted, the only requirement is that the decimal search fails. The fact that you can solve it by another method is irrelevant.

Reply 4

Primus2x

Original post by ghostwalker

From what you've posted, the only requirement is that the decimal search fails. The fact that you can solve it by another method is irrelevant.

Should I mention the actual roots such as pi/2 or can I leave that out?

Reply 5

ghostwalker

Original post by Primus2x

Should I mention the actual roots such as pi/2 or can I leave that out?

No idea. Does the question ask for it?

Reply 6

Primus2x

Original post by ghostwalker

No idea. Does the question ask for it?

It's coursework and the help booklet doesn't tell me how to show the failiure, it shows the steps of doing it with a function that works and the last point tells me to show a function where it doesn't work, my teacher said include the first two iterations I think.

Reply 7

ghostwalker

Original post by Primus2x

...

In open ended questions, I would have thought that the more information you gave that is relevant, the better. I can't see how you would lose marks for it, and you can potentially gain them.

However, I'm not a teacher, nor am I familiar with the coursework, and what is / is not expected.

Mr M

TenOfThem

...

Shameless quotes.

Any thoughts, people?

Reply 8

Mr M

Study Forum Helper

Original post by ghostwalker

Any thoughts, people?

Not on this occasion. This coursework task needs to be completed by the candidate without external help.

I would strongly advise Primus not to submit this particular example as it may identify him or cause his work to come under scrutiny if other readers of this forum decide to copy it.

Reply 9

dada55

If this is the MEI Coursework, then you need a function which cannot be solved algebraically. In factorised form, you will definitely lose the marks. What you need to do is make up a function that has a repeated root at a definite point (not pi etc) that is atleast 3 decimal points and then give the expanded form. The easiest way to do this is to go to wolfram alpha, and keep trying functions of (x+a.bcd)^3 that gives a fairly neat expanded function.
In the whole of the MEI coursework, NEVER show functions factorised.