# Roots

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#1

Iβ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 π
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1 year ago
#2
Iβ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 π
You know the values of and .

The two roots of your new equation are and .

If you add them, and express the result entirely in terms of , 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.

SHORTCUT:

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Since it means that the new roots are and . Rearrange either one for or and sub it into the quadratic since they're roots of it. Multiply through by for the new quadratic in w.
Last edited by RDKGames; 1 year ago
1
#3
Ok Iβve got the right answer now. Thanks a lot π
Last edited by avacados1; 1 year ago
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1 year ago
#4
Ok Iβve got the right answer now. Thanks a lot π
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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#5
(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 π€
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1 year ago
#6
Oh I took the pic, then realised that. And common sense π€
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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#7
(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 π¬ so u can just factor out a k and divide both sides by it.
0
1 year ago
#8
Right π¬ 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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