Roots with conditions (1 Viewer)

[Dumblikeafox]

Current question i'm doing;

Find as a relation between p, q anr r, the condition for the quadratic equation in x

(p^2 - q^2 )x^2 +2q (p + r)x + (q^2 - r^2 = 0) to have equal roots. simplify your answer as far as possible.



Post holiday brain malfunction is upon me, and have no idea what to do. any help would be appreciated

 

[cutemouse]

Discriminant = 0

 

[Dumblikeafox]

b^2-4ac = 0?

 

[Dumblikeafox]

2q(p^2+2pr+r^2) - 4(p^2q^2-q^4+r^2q^2-p^2r^2)=0

 

[Dumblikeafox]

IMO, it's getting worse

 

[cutemouse]

 

[Boxes]

i was expecting a totally different thread, tbh.

 

[Dumblikeafox]

ahh. ok, I'm an idiot

I've been trying to solve that ^ in relation to x.:mad1:

 

[Boxes]

ahh. ok, I'm an idiot

I've been trying to solve that ^ in relation to x.:mad1:

god, how dumb are you?

 

[Dumblikeafox]

i was expecting a totally different thread, tbh.

I'm used to posting catchy titles, often on far more fast moving threads.

 

[Dumblikeafox]

god, how dumb are you?

Sometimes i surprise myself.

Might have something to do with completing from my textbook 11;6,7,8,9 and 16.1through10 in the last day. my mind is a little bit mush

 

[cutemouse]

What were the main differences between the old maths courses (ie. the pre 1981 courses) and the current one?

I know 4U changed alot, like they introduced Volumes, Conic Sections, Additional Complex numbers (eg. DeMoivre's theorem) and Circular motion in mechanics... but I'm not sure how the 2U/3U courses changed.

 

[cutemouse]

There used to be 3D coordinate geometry and Hooke's law which are no longer in the current courses.

Hooke's law... shouldn't that had been in Physics? :S haha But it does explain why Coroneos had a bit on it in his revised book.

What about transformation of axes?

ie. (if I recall correctly) X=xcosθ-ysinθ and Y=xcosθ+ysinθ

I read this is one of Coroneos' books I think.

 

[cutemouse]

I reckon though that sums to products and products to sums should still be taught in 3 unit. (It was originally in 2 unit!)

Hmm, but would it be of much use?

I know in 4U it could be of use for integration... but I don't think I've come across anything in 3U that would require it.

What's the fundemental limit like? Is it much different to the informal treatment of limits we do now?

BTW, I noticed n the 1967 2U paper, 10 marks were given for sketching a simple trig graph and finding the area underneath it between certain limits... Isn't that a bit too easy? lol

 

[cutemouse]

Which do you think is the hardest 2U paper?

 

[cutemouse]

Yes indeed. Products to sums and sums to products is VERY useful and greatly simplifies many things. And this is why it should still be taught.

Do you have an example where it could simplify things? (in the current course)

The fundamental limit is

(provided x is in radians)

Ahh okay... That explains why it is in the Coroneos 2U book, and not in the 3U book.

 

[cutemouse]

Ahh yes first principles for trig functions... I think Coroneos also uses that method. I find that his examples are more systematic than other books, which I like.

What's the tangent rule?

 

[cutemouse]

Nice.. I don't think I did that though..

 

[cutemouse]

Hey Buchnan, you posted the list of topics before here: http://community.boredofstudies.org/238/extracurricular-topics/102519/arc-length.html#post2220688