Polynomials (2 Viewers)

[kawaiipotato]

Can someone read my messy writing and see why my method didn't work? I understand what they did
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The question is for q5 (d) from:
http://4unitmaths.com/2001moriah.pdf

Here are the solutions: http://www.boredofstudies.org/cours...cs_Extension_2_Trial_Paper_Moriah_College.pdf

Thanks

edit: the line above b+c -1 = 0 is Q(x) - 1 = 0 not Q(1)^{-1}

 

[InteGrand]

Can someone read my messy writing and see why my method didn't work? I understand what they did
imgur.com/PYctUtS.jpg
The question is for q5 (d) from:
http://4unitmaths.com/2001moriah.pdf

Here are the solutions: http://www.boredofstudies.org/cours...cs_Extension_2_Trial_Paper_Moriah_College.pdf

Thanks

edit: the line above b+c -1 = 0 is Q(x) - 1 = 0 not Q(1)^{-1}

 

[kawaiipotato]

Ah yeah thanks. Subbed into the equation above that lol.
Lol teacher always said if f (x) is a factor of g (x) then g (x) | f (x). Thanks for the clarification

 

[kawaiipotato]

http://4unitmaths.com/sbhs2002.pdf
Q6 (a) (iii)
There's no solutions and couldn't find my mistake. I got a result that contradicted theirs (I got k<0 for 3 real roots)
Can someone help spot my mistake?
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(ignore the first 5 lines)

 

[atargainz]

http://4unitmaths.com/sbhs2002.pdf
Q6 (a) (iii)
There's no solutions and couldn't find my mistake. I got a result that contradicted theirs (I got k<0 for 3 real roots)
Can someone help spot my mistake?
http://imgur.com/iDPKl4H
(ignore the first 5 lines)

did some algebra wrong finding delta 16-12(4-k) (not sure if that would change the outcome though, didn't try, just had a quick skim)

 

[kawaiipotato]

did some algebra wrong finding delta 16-12(4-k) (not sure if that would change the outcome though, didn't try, just had a quick skim)

Yep the sign of k changes. Thanks

Can someone show me how to do Q8 (a) (i)?

 

[integral95]

I don't think the roots of the derivative having opposite signs would imply the original function having 3 real roots,

It should be the stationary points with the y-values being opposite in signs giving 3 roots.

EDIT: besides the better method is to draw the graph k/x, one case where k>0 and k<0 and observe the intersection with the graph you drew

 

[kawaiipotato]

I don't think the roots of the derivative having opposite signs would imply the original function having 3 real roots,

It should be the stationary points with the y-values being opposite in signs giving 3 roots.

Oh yeah. I should've subbed those roots into y.
That seems long, is there another method?

 

[integral95]

Oh yeah. I should've subbed those roots into y.
That seems long, is there another method?

the better method is to draw the graph k/x, one case where k>0 and k<0 and observe the intersection with the graph in part ii)

.

 

[kawaiipotato]

Can someone show me how to do Q8 (a) (i)?

Is this a valid method?
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oops, replace every theta with an 'x'

 

[InteGrand]

Is this a valid method?
www.imgur.com/Fzdom2h
oops, replace every theta with an 'x'

Yeah that's a valid method.