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# c1 - roots? watch

1. What does it mean to write down the roots?

For example, http://www.mei.org.uk/files/papers/c107ja_3hoza9.pdf

Question 13 (iii)
2. where the function F(x) crosses the x axis
Spoiler:
Show
there is a root at 5
3. (Original post by Slenderman)
What does it mean to write down the roots?

For example, http://www.mei.org.uk/files/papers/c107ja_3hoza9.pdf

Question 13 (iii)
The roots of are precisely . That is, "find the roots of " means "solve ".
4. (Original post by Tom 97)
where the function F(x) crosses the x axis
Spoiler:
Show
there is a root at 5
Oh okay, how did you know 5 was a root? Do you divide it by (x-3) ? Did you just guess 5? What's the method?
5. (Original post by Slenderman)
Oh okay, how did you know 5 was a root? Do you divide it by (x-3) ? Did you just guess 5? What's the method?
You know the roots of f(x) so how can you find the roots of f(x-3)?

Think about what f(x-3) looks like compared to f(x) and how the roots will move.
6. Okay so since 5 was a root, I divied by x-5 and got the quadratic and got the final root.

But in the exam, are you just meant to try random numbers til you find one? Is there a way of finding that 5 the first time round?
7. (Original post by notnek)
You know the roots of f(x) so how can you find the roots of f(x-3)?

Think about what f(x-3) looks like compared to f(x) and how the roots will move.
Oh I see, thanks got it.
8. (Original post by Slenderman)
Oh okay, how did you know 5 was a root? Do you divide it by (x-3) ? Did you just guess 5? What's the method?
I dont do OCR MEI, but from question 13)i you get 2 x values (roots), which is f(x). f(x-3) is just a transformation of the graph. Translation 3 units in positive x direction. So for f(x), x=2, then for f(x-3), x= 2+3= 5
9. (Original post by Slenderman)
Oh okay, how did you know 5 was a root? Do you divide it by (x-3) ? Did you just guess 5? What's the method?
Your know that x=2 is a root of the original formula.
As you are told to find the roots of f(x-3) you are in effect moving the graph 3 places to the right (Adding 3 to the x value).
Hence you end up with 2+3=5
Therefore a root of f(x-3) is 5.
Hope this helps!
10. (Original post by Smaug123)
The roots of are precisely . That is, "find the roots of " means "solve ".

(Original post by notnek)
You know the roots of f(x) so how can you find the roots of f(x-3)?

Think about what f(x-3) looks like compared to f(x) and how the roots will move.
Sorry to be picky, but an equation has roots; a function has zeros.
So you can find the roots of f(x) = 0 or the zeros of f(x), but not the "roots of f".

(I'm sure you guys know this anyway )
11. (Original post by davros)
Sorry to be picky, but an equation has roots; a function has zeros.
So you can find the roots of f(x) = 0 or the zeros of f(x), but not the "roots of f".

(I'm sure you guys know this anyway )
I've seen the two words used interchangeably by textbooks and professional mathematicians:

http://en.wikipedia.org/wiki/Zero_of_a_function
12. (Original post by notnek)
I've seen the two words used interchangeably by textbooks and professional mathematicians:

http://en.wikipedia.org/wiki/Zero_of_a_function
Maybe I just have higher standards than they do?

You'll be telling me next it's OK to spell "shew" as "show"!
13. (Original post by davros)
Maybe I just have higher standards than they do?

You'll be telling me next it's OK to spell "shew" as "show"!
Zounds, man - methinks art over-progressive!

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