how to do this?

[fallen crater]

I want to understand binomial or any trick for this one

[forest shale]

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[flat ridge]

What is the degree of this polynomial?

[fallen crater]

x^50

[worldly mesa]

and to get the x^49 term you have to pick x in 49 of the terms

in how many ways can you do this?

[fallen crater]

if the order doesn't matter here i will pick

50C49
50C1 =50

[worldly mesa]

and with each choice you pick exactly one of the coefficients

-99, -97, -95 etc etc

[flat ridge]

there is a relationship between the second last coefficient and the roots

more commonly known as Vieta's formula

incidentally proven with aL's method

[pearl musk]

for a degree n to find the value of the n-1 given its factored form its just the sum of the roots multiplied by negative 1

[fallen crater]

Multiplication of roots or sum?

[flat ridge]

Which?

[fallen crater]

...

[flat ridge]

It is important for you to know this

If you don't, please look up Vieta's formulas on the internet

[fallen crater]

Bro i know vietta formulas and i have used it@flat ridge

Just wonder what you said🤔

Second last cofficent?

[flat ridge]

Well I asked, how can the second last coefficient be computed from the roots?

[fallen crater]

No idea

I am not understanding the question actually properly

[flat ridge]

Well what we have so far is that

the polynomial is of degree 50

and we want to find the coefficient of x^49

which corresponds to the second last coefficient of this polynomial

and how do you find this second last coeff with Vieta's formula?

[fallen crater]

I only read that sum/multiplication of roots by vieta but never read such second last coffee

[fallen crater]

Please send a link. I am stuck

[worldly mesa]

(x-1)(x-2)(x-3), what is the coefficient of x^2

then apply the same principle to the big polynomial you got in the first post

or if that's too easy

(x-1)(x-3)(x-5)(x-7)(x-9) and find coefficient of x^4

you don't need to know anything about viete's theorem to solve this problem

[fallen crater]

I will multiply all of these and then see

[fallen crater]

all the x have no coefficient into multiplication so it will be 1

1×x^4

[worldly mesa]

there are 5 terms

so it's deg 5 polynomial

[fallen crater]

Ohh i thought four

Then i will multiply all of these and then see

It will take a 20 minutes

[worldly mesa]

that's too much effort

you dont need all the coefficients

just coefficient of x^4

[fallen crater]

Yes

I want to learn the method

How you count?

Directly

[worldly mesa]

how do you get a summand with x^4?

you pick x 4 times

and constant for the last term

[fallen crater]

Yeah

[worldly mesa]

so it will be

[fallen crater]

constant last term for x^0

[worldly mesa]

-1x^4 -3x^4 - 5x^4 - 7x^4 -9x^4

do you understand now?

[fallen crater]

(x-1)(x-3)(x-5)(x-7)(x-9)

Hang on

[fallen crater]

Not understanding

Sorry

[worldly mesa]

then think about it

[fallen crater]

What I think

I have no clear idea

Only can see five terms and choosing four

[worldly mesa]

yes

[fallen crater]

Let me write it wait

I got positive

There will be more. Cases

[fallen crater]

And here you got -1 wow

[worldly mesa]

because the coefficients are all negative

if you do (x-1)(x-3) and want coefficient of x you still do the same thing

-1x -3x

[pearl musk]

so lets look at (x-u)(x-v)

what is the value of the x term?

[fallen crater]

x^2-vx-ux+uc=x^2-(v+u)x+uv

Clearly -(v+u)

[pearl musk]

yeah

what about (x-u)(x-v)(x-w)?

[fallen crater]

X^3?

Or x^2

i will need to multiply all of these then i can tell

[fallen crater]

Where is your -1

@worldly mesa

[worldly mesa]

that's what we're trying to tell you

you dont NEED to multiply it all

[pearl musk]

let me show him so he sees for himself

[fallen crater]

Yes i don't need

[pearl musk]

because this’ll give him the answer he is looking for

[fallen crater]

But you guys are not making the method clear by step by step

[pearl musk]

expand the cubic expression

what do you get?

[fallen crater]

Instead of rounding on the same thing

[fallen crater]

Multiply

[pearl musk]

what do you get though

[worldly mesa]

you are not calculating correctly, I am not responsible for that

[fallen crater]

(x-u)(x-v)(x-w)
(x^2-vx-ux+uv)(x-w)
(x^2-(v+u)x+uv)(x-w)

-wx^2-(v+u)x^2

-(v+u+w)x^2

[fallen crater]

Lmaooooo

i took four out of five

[pearl musk]

okay, so what are you seeing

[fallen crater]

And then i have shown you see x^4 is positive

[fallen crater]

Now i am feeling there is something good

We just need to sum

And put a negative sign

[worldly mesa]

,w (x-1)(x-3)(x-5)(x-7)(x-9)

[fallen crater]

Take four terms

[worldly mesa]

blah

wolfram..

[fallen crater]

Lol

Wolf

[worldly mesa]

the x^4 term is -25

[fallen crater]

Wolf in fran

[worldly mesa]

-1-3-5-7-9 = -25

[fallen crater]

No i am not saying for this

I show you that we take four terms out of five

[pearl musk]

@fallen crater so basically what did you notice about the terms of the expressions you expanded

[fallen crater]

i can do it directly now

i will sum all of these and then negative sign

[worldly mesa]

answer me then, why do we take 4 out 5? why not 3 out of 5?

[pearl musk]

yes

[fallen crater]

And one more thing i remembered now by vietta

The second term is always the sum of roots

[pearl musk]

yes

[fallen crater]

which is one less power

-b/a

[worldly mesa]

dont need to worry about that right now

[fallen crater]

Ohhh god

[pearl musk]

thats what i was getting you to understand

[fallen crater]

i got it now what you guys were pointing

Sooo x^50 terms

[worldly mesa]

so, can you answer the initial question now?

[fallen crater]

Now i need x^49

So i will sum

1+3+5+7.....99 and then negative sign

[worldly mesa]

indeed

[pearl musk]

yes

[worldly mesa]

you dont need viete to conclude this

basic arithmetic is enough

[fallen crater]

50^2 sum of odd terms

-2500 C

Boom

[worldly mesa]

sum of arithmetic progression

[fallen crater]

50/2 [2+49×2]=25×100

Same thing

-2500

[pearl musk]

yup

[fallen crater]

actually when i removed one term out of five i got x^4 abosulety

Which will be positive

So i misunderstood i gues

[worldly mesa]

you cant have different result

the polynomial is given from the start

it doesn't change

[fallen crater]

I want to understand it

Now

😂😋😋

[worldly mesa]

you already do

[fallen crater]

i guess you multiplied and put -1

[worldly mesa]

i multiply them such that I pick x in 4 terms

[fallen crater]

Hmm

Nice

[worldly mesa]

and the coefficient (which is negative) as 5th

(x-1)(x+2)(x-6)(x+7)(x-11)

x^4 term is -1+2-6+7-11

[fallen crater]

And a negative sign

Hmm

Interesting

Now i am feeling we form formulas

[worldly mesa]

i dont memorise formulas, maybe it is maybe it isnt

idc

[worldly mesa]

what negative sign?

i simply add the coefficients together the way they appear

that's all

[fallen crater]

+close