Polynomials >.> (1 Viewer)

[mathsnoob]

Hello all!

Kinda need help with some 4U maths questions!

1. Write (3x^2 + 4x - 6) / (x-1)^2 (x+2) as partial fractions
2. If a,b and c are the roots of x^3 + 2x^2 -3x-1 =0 then find the eqn whose roots are (ab/c), (bc/a) and (ac/b).

Thank you everyone who helps!!!

 

[blaze.bluetane]

 

[lychnobity]

Hello all!

Kinda need help with some 4U maths questions!

1. Write (3x^2 + 4x - 6) / (x-1)^2 (x+2) as partial fractions
2. If a,b and c are the roots of x^3 + 2x^2 -3x-1 =0 then find the eqn whose roots are (ab/c), (bc/a) and (ac/b).

Thank you everyone who helps!!!

Seeing as blaze.bluetane beat me to no.2 :

1) (-2/9)/(x+2) + (1/3)/(x-1)² + (29/9)/(x-1)

Use the mental method

 

[jet]

blaze.bluetane: Just a quick comment. When you take the square root, it should be positive and negative i.e ± 1/sqrt(y). The rest works the same, and the ± cancels when you square both sides of the new equation. Just make sure you maintain the correct order of +s and -s. I actually lost a mark in an exam last year because I forgot the ±

 

[blaze.bluetane]

blaze.bluetane: Just a quick comment. When you take the square root, it should be positive and negative i.e ± 1/sqrt(y). The rest works the same, and the ± cancels when you square both sides of the new equation. Just make sure you maintain the correct order of +s and -s. I actually lost a mark in an exam last year because I forgot the ±

too right. thank you!

matter of fact I got 79/80 in my last assessment task...

forgot to take pos/neg of a complex square root

equating real and imaginary components..

x^2 - y^2 = 5
xy=6

therefore x=3, y=2

root=3+2i

.....FAIL

 

[blaze.bluetane]

Seeing as blaze.bluetane beat me to no.2 :

1) (-2/9)/(x+2) + (1/3)/(x-1)² + (29/9)/(x-1)

Use the mental method

Heaviside's Rule??

 

[jet]

too right. thank you!

matter of fact I got 79/80 in my last assessment task...

forgot to take pos/neg of a complex square root

equating real and imaginary components..

x^2 - y^2 = 5
xy=6

therefore x=3, y=2

root=3+2i

.....FAIL

Lol, silly mistake. We all do weird things under exam conditions.

 

[gurmies]

Nothing can compare to my integration fail in the last assessment. Essentially I ended up with something in the form A/(A+B) and called it 1 + A/B...

 

[jet]

Well, I happened to skip a whole part of a question in my 4u HSC, because I didn't notice it.

 

[gurmies]

Ouch

 

[lychnobity]

Heaviside's Rule??

eh? I think it's some sort of variant of it

The method I used is just called the "mental method" in Terry Lee's textbook.