sum & products of roots notation (1 Viewer)

[ilovemangos]

hi, i was wondering if its allowed to write

to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and

for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

 

[cossine]

hi, i was wondering if its allowed to write
View attachment 41487
to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and
View attachment 41488
for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

I would not use this notation without first defining it.

If you don't want to do this I would write:

sigma alpha_i * alpha_j (condition i < j)

Note that we can't write

sigma alpha_i * alpha_j (condition i != j)

Because this will return all the permutations

 

[appleali]

hi, i was wondering if its allowed to write
View attachment 41487
to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and
View attachment 41488
for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

I wouldn't use this, its ambiguous, just say sum of roots or literally alpha + beta + gamma for cubics or alpha + beta + gamma + delta (I've never seen any sums/products of root questions beyond quartics so it's highly unlikely that the 5 seconds you save from this outweighs the risk of the marker not understanding)

Basically don't bloat your answers with mathematical kafaffle, just keep it chill

 

[appleali]

hi, i was wondering if its allowed to write
View attachment 41487
to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and
View attachment 41488
for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

If you really wanted to use the notation, to keep it consistent for product of roots you could use capital pi (which is like sigma but multiplying consecutive terms instead of adding)

 

[Drongoski]

hi, i was wondering if its allowed to write
View attachment 41487
to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and
View attachment 41488
for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

These are well-established conventions. But I don't know if you'd be penalised for their use in your HSC exams. If I were a marker, I'd accept it. But it is possible some markers are themselves not familiar with this shorthand and be confused; but most "smart enough" markers should be able to figure this out as it is a nice compact notation.

Some students were wondering if you are allowed to use "cis A" instead of "cos A + i sin A". Any examination regime that disallows this, is, to me, plain idiotic.


Note:
I first came across this notation in a classic Algebra textbook : "Higher Algebra by Hall & Knight (Publisher: MacMillan & Co), 1st Edition: 1887!", which I have in my collection.

 

[ilovemangos]

Alright thank you all for the information, I will probably use this shorthand for internals because my teachers accept it. Then for externals, I'll use the words.

 

[appleali]

Alright thank you all for the information, I will probably use this shorthand for internals because my teachers accept it. Then for externals, I'll use the words.

No problem

 

[Average Boreduser]

hi, i was wondering if its allowed to write
View attachment 41487
to denote sum of roots, instead of writing "sum of roots: " (sorry im lazy)
and
View attachment 41488
for sum of roots 2 at a time
etc.
though i'm not sure how i would express the product of roots like that, ill probably just write that one. thankyou

My maths teacher (whos been a hsc marker for 20 yrs now) uses this notation.... unless your marker is unfamiliar with a format as common as the ones youve provided, I can't see how you'd be penalised...

 

[appleali]

I suppose if the notation were to be used many times throughout a question, you can define it at the start and then use it, like \sigma alpha = sum of roots. But then, you could just use an ever shorter shorthand like a single letter variable