Need URGENT!! help on MFP2 question

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mathsRus
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Hi guys

I have exam tomorrow and I cannot understand Q8(di, dii) on AQA Jan 2011. The mark scheme is too complicated.

http://filestore.aqa.org.uk/subjects...W-QP-JAN11.PDF

I am also stuck on this roots of polynomial question Q4(aiv, b) on this paper:

http://filestore.aqa.org.uk/subjects...W-QP-JUN11.PDF



Thanks
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brianeverit
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(Original post by mathsRus)
Hi guys

I have exam tomorrow and I cannot understand Q8(di, dii) on AQA Jan 2011. The mark scheme is too complicated.

http://filestore.aqa.org.uk/subjects...W-QP-JAN11.PDF

I am also stuck on this roots of polynomial question Q4(aiv, b) on this paper:

http://filestore.aqa.org.uk/subjects...W-QP-JUN11.PDF



Thanks
For first question, the equation is a sixth degree equation but there will be no z^5 term and the sum of the roots is given by  - coefficient\ of\ z^5 \ divided \ by \ coefficient of\ z^6
note then that the sum of the real parts of the roots must be zero, and that is a sum of cosines. Can you get anywhere from that?
For the second question, noter that if  \alpha,\beta\text{ and }\gamma \text{ are the roots, then }
 \alpha^3-2\alpha^2+k=0, \beta^3-2\beta^2+k=0 \text{ and }\gamma^3-2\gamma^2+k=0
Just add them together.
Similarly for 4th powers since \alpha , \beta, \gamma must also be roots of  z^4-2z^3+kz=0
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mathsRus
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(Original post by brianeverit)
For first question, the equation is a sixth degree equation but there will be no z^5 term and the sum of the roots is given by  - coefficient\ of\ z^5 \ divided \ by \ coefficient of\ z^6
note then that the sum of the real parts of the roots must be zero, and that is a sum of cosines. Can you get anywhere from that?
For the second question, noter that if  \alpha,\beta\text{ and }\gamma \text{ are the roots, then }
 \alpha^3-2\alpha^2+k=0, \beta^3-2\beta^2+k=0 \text{ and }\gamma^3-2\gamma^2+k=0
Just add them together.
Similarly for 4th powers since \alpha , \beta, \gamma must also be roots of  z^4-2z^3+kz=0
I am sorry, I still didn't understand it. This is my weakest chapter where I just don't understand stuff.

If you can explain it as if you were explaining it to a new learner would be helpful.

Thanks
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davros
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(Original post by mathsRus)
Hi guys

I have exam tomorrow and I cannot understand Q8(di, dii) on AQA Jan 2011. The mark scheme is too complicated.

http://filestore.aqa.org.uk/subjects...W-QP-JAN11.PDF

I am also stuck on this roots of polynomial question Q4(aiv, b) on this paper:

http://filestore.aqa.org.uk/subjects...W-QP-JUN11.PDF



Thanks
For Q8, what term in a polynomial do you normally look at to see what the sum of the roots is? Does that term exist in the given polynomial when you expand the bracket? So what can you deduce about the sum of roots?

For Q4, aiv, the equation you proved in (iii) holds equally for beta and gamma. So just add up the 3 versions of equation (iii) and see what drops out!

For (b), start by multiplying the equation (iii) by alpha to give you one equation. Again, you could equally have started with a version of (iii) with alpha replaced by beta or gamma, so you can write down 2 other versions of your new equation straight away. Add up your 3 new equations and use the information from previous parts of the question.

I haven't tried (b)(ii) but I'd expect it to go a similar way (in fact, try multiplying (iii) by alpha squared this time to get a new equation of degree 5 and write down 2 similar equations in beta and gamma, then add them - I think that will do the trick!)
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mathsRus
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I figured out Q4 but still do not understand Q8
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davros
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(Original post by mathsRus)
I figured out Q4 but still do not understand Q8
Think back to when you did quadratics.

When you expand (x-a)(x-b) you get x^2 - (a+b)x + ab, so the sum of the roots (a+b) is minus the coefficient of the 2nd term (the one with x in).

Where do you find the sum of roots in higher degree equations?
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