as further maths roots of polynomial Watch

Janej77
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I am struggling with 8d and e. Can someone help plz?
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Janej77
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Help plz
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Janej77
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Bump
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RuneFreeze
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Sorry can't really help you haven't done this chapter yet
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Janej77
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Anyone done this before?
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ralph9694
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I did this in November/December I think, I haven't been able to do d yet but I just got e and it's correct according to the book.
What have you tried so far?
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S2M
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RDKGames ghostwalker
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Janej77
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(Original post by ralph9694)
I did this in November/December I think, I haven't been able to do d yet but I just got e and it's correct according to the book.
What have you tried so far?
I got to (-3/4)^2- 6(4/3) but I got terms afterwards to get to the answer for the question that I can’t factorise. Can u show me method for e? I can’t work it out
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ralph9694
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for e I started out expanding  (\alpha\beta\gamma + \alpha\beta\delta + \alpha\gamma\delta + \beta\gamma\delta)^2 and the comparing that to what is in the question
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Janej77
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(Original post by ralph9694)
for e I started out expanding  (\alpha\beta\gamma + \alpha\beta\delta + \alpha\gamma\delta + \beta\gamma\delta)^2 and the comparing that to what is in the question
Thanks I’ll try that out. Have u got anywhere with d?
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ralph9694
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I'm trying a similar thing, expanding another squared bracket, 6 terms in each, so it's taking a while.
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blockingHD
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(Original post by ralph9694)
for e I started out expanding  (\alpha\beta\gamma + \alpha\beta\delta + \alpha\gamma\delta + \beta\gamma\delta)^2 and the comparing that to what is in the question
And do the same for (\sum \alpha\beta)^{2}
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Janej77
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(Original post by blockingHD)
And do the same for [latex](\sum_\alpha\beta)^{2}[\latex]
That’s the bit where I am stuck. I worked all that out but I can’t factorise them into the values I know. Not all the algebra have the same letter.
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ralph9694
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with part e, after expanding the brackets, ignoring the (\alpha\beta\gamma)^2 terms, try taking out a common factor (one should jump out) of everything left over
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Janej77
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(Original post by ralph9694)
with part e, after expanding the brackets, ignoring the (\alpha\beta\gamma)^2 terms, try taking out a common factor (one should jump out) of everything left over
Thanks I ve got the right answer for e now
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ralph9694
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I just got it for d using the same method
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Janej77
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(Original post by ralph9694)
I just got it for d using the same method
What is the common factor? I can’t seem to find it
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ralph9694
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I think for d it's a bit harder, I initially saw the  \alpha\beta\gamma\delta and put it aside as we are told what it's value is, but I realised it was useful to add 2 more of it if that makes sense, and then factorise from there.
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Sir Cumference
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(Original post by Janej77)
I am struggling with 8d and e. Can someone help plz?
For d, If you've covered the substitution method a much less tedious method for this question is to first write out the quartic polynomial in the form

x^4 + bx^3 + cx^2 + dx + e

Then find the polynomial with roots \alpha^2, \beta^2, \gamma^2 and \delta^2 by using substitution.

You'll only need to find the coefficient of x^3 in this polynomial since this will be equal to -\sum \alpha^2\beta^2 which is what you need.

And part e can be done in a similar way.

If you've covered the substitution method and want more help with this then let me know.
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Sir Cumference
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(Original post by Janej77)
How would I go on to find sum alpha ^2 beta ^2? I’ve learned substitution for linear transformation
Do you know how to find a polynomial with roots \alpha^2, \beta^2, \gamma^2, \delta^2 if you have the polynomial with roots \alpha, \beta, \gamma, \delta?

Then in this new polynomial the sum of the product of two roots i.e. \alpha^2\beta^2 + \alpha^2\gamma^2 + ... is what the question is asking for.

So you need to find the coefficient of x^3 in this new polynomial.
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