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OCR MEI FP1 - roots of equations watch

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    the roots of the quadratic equation 2z^2+5z-9 = 0 are \alpha\ and \beta

    find the quadration equation with the roots  3\alpha and 3\beta past the quadratic formula part to find the roots, i do not have a clue
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    What do you know about b and c in terms of alpha and beta for quadratic equations?
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    -b/a = sum, c/a = product?
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    Yep, so you should be ok!

    You have a+b = -5/2 and ab = -9/2 from the old equation. And you know that the new equation has 3a + 3b = -b/a and 9ab=c/a so you just need to do a bit of rearranging.
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    (Original post by jonny23563)
    Yep, so you should be ok!

    You have a+b = -5/2 and ab = -9/2 from the old equation. And you know that the new equation has 3a + 3b = -b/a and 9ab=c/a so you just need to do a bit of rearranging.
    sorry im really not following :\
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    Right, I've just realised that I used a and b for two completely different things. We have

    \alpha +\beta= \frac{-5}{2} and \alpha\beta = \frac{-9}{2}.

    We know the new equation needs roots 3\alpha, 3\beta. So the b and c of the quadratic equation will be \frac{b}{a} = 3\alpha + 3\beta = 3(\alpha+\beta) and \frac{c}{a} = 9\alpha\beta. So you can substitute and you're done!
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    what the hell, 9ab ?? so thats what went wrong

    what about a-2 and b-2

    this chapter is really killing me :|
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    There's another method you could use.

    could say let w = 3x
    so x = w/3. so the new equation is found by subbing in w/3 for x.

    and yeah I hate this chapter as well. luckily though, and I'd like someone to cornfirm this for me, the questions in the fp1 book don't come up barely at all, and in the fp1 exam it's mostly something like "find new equation with these roots.."
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    (Original post by Tallon)
    There's another method you could use.

    could say let w = 3x
    so x = w/3. so the new equation is found by subbing in w/3 for x.

    and yeah I hate this chapter as well. luckily though, and I'd like someone to cornfirm this for me, the questions in the fp1 book don't come up barely at all, and in the fp1 exam it's mostly something like "find new equation with these roots.."
    i cant even remember having to go over a chapter this much, the maths is so weird.. and i hope thats the case !
 
 
 
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Updated: March 17, 2009

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