RickHendricks
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roots of polynomials question:

1. The quadratic equation, ๐‘ฅ2+๐‘˜๐‘ฅ+2๐‘˜=0, where k is a non-zero constant, has roots ๐›ผ+๐›ฝ. Find a quadratic equation (in terms of k) with roots ๐›ผ/๐›ฝ ๐‘Ž๐‘›๐‘‘๐›ฝ/๐›ผ.

no idea where to start please help

Thanks
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RDKGames
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(Original post by RickHendricks)
roots of polynomials question:

1. The quadratic equation, ๐‘ฅ2+๐‘˜๐‘ฅ+2๐‘˜=0, where k is a non-zero constant, has roots ๐›ผ+๐›ฝ. Find a quadratic equation (in terms of k) with roots ๐›ผ/๐›ฝ ๐‘Ž๐‘›๐‘‘๐›ฝ/๐›ผ.

no idea where to start please help

Thanks
The first thing is to write down \alpha + \beta and \alpha \beta in terms of k.
Then note that the new equation will have the coefficient of x as - \left( \dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} \right) and the constant as \dfrac{\alpha}{\beta} \cdot \dfrac{\beta}{\alpha} - so you want to start finding these in terms of \alpha \beta and \alpha + \beta which you know in terms of k

Also, post your maths questions in the maths forum.
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Lemur14
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(Original post by RickHendricks)
roots of polynomials question:

1. The quadratic equation, ๐‘ฅ2+๐‘˜๐‘ฅ+2๐‘˜=0, where k is a non-zero constant, has roots ๐›ผ+๐›ฝ. Find a quadratic equation (in terms of k) with roots ๐›ผ/๐›ฝ ๐‘Ž๐‘›๐‘‘๐›ฝ/๐›ผ.

no idea where to start please help

Thanks
I'm assuming that's has a root of alpha and a root of beta?
If so, since -k=the sum of the roots
And 2k= the product of the roots
then you have values to match to k
Then, you'll want to find the new sum of the roots, and product of the roots with the roots alpha/beta and beta/alpha. You can put these in terms of k as you have calculated above.
Then form the new equation x^2 -(sum of the roots) + (products of the roots) = 0
Hope that makes sense
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RickHendricks
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(Original post by RDKGames)
The first thing is to write down \alpha + \beta and \alpha \beta in terms of k.
Then note that the new equation will have the coefficient of x as - \left( \dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} \right) and the constant as \dfrac{\alpha}{\beta} \cdot \dfrac{\beta}{\alpha} - so you want to start finding these in terms of \alpha \beta and \alpha + \beta which you know in terms of k

Also, post your maths questions in the maths forum.
what is alpha + beta though? We are just told the roots are alpha+beta, not that the actual roots are alpha and beta
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RDKGames
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(Original post by RickHendricks)
what is alpha + beta though? We are just told the roots are alpha+beta, not that the actual roots are alpha and beta
Pretty sure that plus is supposed to be a comma.
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RickHendricks
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(Original post by RDKGames)
Pretty sure that plus is supposed to be a comma.
nope. That's what i'm confused at.

It says alpha+beta.

I asked all the senior maths prefects in my school and neither of them could do it.
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RDKGames
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(Original post by RickHendricks)
nope. That's what i'm confused at.

It says alpha+beta.

I asked all the senior maths prefects in my school and neither of them could do it.
Then the question as it stands does not make sense.
It could, however, mean that the quadratic has equal roots which are x=\alpha + \beta in which case we would get x^2+kx+2k=x^2-2(\alpha + \beta)x+(\alpha + \beta)^2 but it could be worded MUCH better if that is the case.
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RickHendricks
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(Original post by RDKGames)
Then the question as it stands does not make sense.
It could, however, mean that the quadratic has equal roots which are x=\alpha + \beta in which case we would get x^2+kx+2k=x^2-2(\alpha + \beta)x+(\alpha + \beta)^2 but it could be worded MUCH better if that is the case.
so how would we write it as alpha/beta then it the roots r alpha + beta
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RDKGames
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(Original post by RickHendricks)
so how would we write it as alpha/beta then it the roots r alpha + beta
Upon actually looking at it, it seems that this is nonsense as well. So this isn't what was meant either.

Just imagine there's a comma instead of a plus and move on.

What's the official answer, if there is one?
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Sir Cumference
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(Original post by RickHendricks)
roots of polynomials question:

1. The quadratic equation, ๐‘ฅ2+๐‘˜๐‘ฅ+2๐‘˜=0, where k is a non-zero constant, has roots ๐›ผ+๐›ฝ. Find a quadratic equation (in terms of k) with roots ๐›ผ/๐›ฝ ๐‘Ž๐‘›๐‘‘๐›ฝ/๐›ผ.

no idea where to start please help

Thanks
Can you please post a picture of the question?
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