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    What does it mean to write down the roots?

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

    Question 13 (iii)
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    where the function F(x) crosses the x axis
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    there is a root at 5
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    (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 f: \mathbb{R} \to \mathbb{R} are precisely \{x \vert f(x) = 0 \}. That is, "find the roots of f" means "solve f(x) = 0".
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    (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?
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    (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.
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    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?
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    (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.
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    (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
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    (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!
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    (Original post by Smaug123)
    The roots of f: \mathbb{R} \to \mathbb{R} are precisely \{x \vert f(x) = 0 \}. That is, "find the roots of f" means "solve f(x) = 0".

    (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 )
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    (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
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    (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"!
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    (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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