• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

Preliminary mathematics marathon (2 Viewers)

kooliskool

Member
Joined
Nov 23, 2006
Messages
138
Gender
Male
HSC
2007
lol what expand ( p -a) ( p-b) (p-c) ( p-d), where a, b, c, d are roots


its a little less work i guess
There's actually another way that only takes really a few lines only,

If you look at the as product of roots, we can create a new equation with as roots like follows:

The relationship between the new roots and the old one is

Hence

Substitute this back into the old equation which will be:



and expand to get the leading coefficient and the constant term will give you the product of roots then.

Leading coefficient will be:

Constant Term will be:

So if I'm not mistaken, is the answer just 1?
 

SpiralFlex

Well-Known Member
Joined
Dec 18, 2010
Messages
6,960
Gender
Female
HSC
N/A
shameless revive

spiralflex or someone, get in here
Yes Sir!

a) Since it is Preliminary, Preliminary student's only answer this!

I will start with a basic question.

Express the following fraction in the partial form,

. Where and are constants.


The fraction is


For Preliminary students,

b) The roots of the equation are in the ratio of . Show that


For HSC students, [Sorry this question was on the thread already. Didn't know. Attempt it if you want anyway. No cheating. :)]

c) Differentiate with respect to ,

. Hence find the differential coefficient of

[Hint: Don't differentiate normally.]


For HSC students,

d) Show that and hence evaluate

Remarks: HSC students! Don't answer the Preliminary sections! Preliminary students! Attempt HSC questions if you can!
 
Last edited:

Drongoski

Well-Known Member
Joined
Feb 22, 2009
Messages
4,254
Gender
Male
HSC
N/A
c) is a very interesting question.
 
Last edited:

AAEldar

Premium Member
Joined
Apr 5, 2010
Messages
2,246
Gender
Male
HSC
2011
I think I've still got the working for b) on my pc. I shall let someone else answer it though.

Well, it's question c now.
 

Hermes1

Banned
Joined
Oct 4, 2010
Messages
1,282
Gender
Male
HSC
2011
Find the value of k:
The remainder is 25 when:
is divided by
I know P(k) = 25 but im unsure what to do after.
sub in x = k, then get a quadratic equation in terms of k^2 and solve it, then you should get 4 solutions for k.
 

Drongoski

Well-Known Member
Joined
Feb 22, 2009
Messages
4,254
Gender
Male
HSC
N/A




Note: for real k (no complex for MX1):

 
Last edited:

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top