avacados1
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I’d usually say w= however the original root (x) has been changed and then make x the subject. I would then sub that back into the original equation. But with this I donno how to go abouts it. Any help appreciated πŸ™‚
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RDKGames
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(Original post by avacados1)
I’d usually say w= however the original root (x) has been changed and then make x the subject. I would then sub that back into the original equation. But with this I donno how to go abouts it. Any help appreciated πŸ™‚
You know the values of \alpha + \beta and \alpha\beta.

The two roots of your new equation are \dfrac{\alpha + \beta}{\alpha} and \dfrac{\alpha + \beta}{\beta}.

If you add them, and express the result entirely in terms of \alpha + \beta,\alpha \beta, then you can easily determine what this sum is in terms of k. This result is the -ve coefficient of x in your new quadratic.

Repeat similarly for their product. This in terms of k will be the constant term of your quadratic.

Hence just write down what this new quadratic is.


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Since \alpha + \beta = -2k it means that the new roots are w = \dfrac{-2k}{\alpha} and w = \dfrac{-2k}{\beta}. Rearrange either one for \alpha or \beta and sub it into the quadratic since they're roots of it. Multiply through by w^2 for the new quadratic in w.
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avacados1
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Ok I’ve got the right answer now. Thanks a lot πŸ™‚
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RDKGames
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(Original post by avacados1)
Ok I’ve got the right answer now. Thanks a lot πŸ™‚
You have a factor of k in there which you can get rid off.

Bonus credit for correctly reasoning why we can divide it out.
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avacados1
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(Original post by RDKGames)
You have a factor of k in there which you can get rid off.

Bonus credit for correctly reasoning why we can divide it out.
Oh I took the pic, then realised that. And common sense πŸ€”
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RDKGames
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(Original post by avacados1)
Oh I took the pic, then realised that. And common sense πŸ€”
Common sense would also tell you that the infinite sum

1 + 1/2 + 1/3 + 1/4 + ...

converges onto some number, but it doesnt

So unfortunately thats not the right reasoning here.
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avacados1
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(Original post by RDKGames)
Common sense would also tell you that the infinite sum

1 + 1/2 + 1/3 + 1/4 + ...

converges onto some number, but it doesnt

So unfortunately thats not the right reasoning here.
Right 😬 so u can just factor out a k and divide both sides by it.
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RDKGames
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(Original post by avacados1)
Right 😬 so u can just factor out a k and divide both sides by it.
You can only divide by something when you know its non-zero, so its just a matter of understanding why k cannot be zero before you divide by it.
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