algebra doubt

[pastel igloo]

<@&1227988399579730072>

Note for OP

+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.

[north raven]

Wait how do i delete the thread 🥲

[placid sky]

If a0 , a1 , . . . , an are constants and n is a nonnegative integer, then the function

f(x)=anxn +an−1xn−1 +···+a1x+a0

is called a polynomial.

ai can be real or imaginary, that we the polynomial can be with real coefficient or im coefficients

Can have im roots as well

Also, x-pi=0 is a polynomial with a transcendental number as its solution

[north raven]

here, why is dividing the coefficients into a<↓k>(n) preferred?

[placid sky]

We get Rational functions by diving two polynomials
p(x)/q(x)
Ofc q(x) is non zero

[placid sky]

Didn’t get you

[north raven]

You represented the coefficients of the terms of a polynomial as the product of two values

[placid sky]

No no

🥲🥲

[north raven]

a1 and n for example

[placid sky]

It’s subscript

a sub 1

[north raven]

oh 🥲

[placid sky]

Just different coefficients hehe

[north raven]

I'm sorry

[placid sky]

No worries :)

Whats left

[north raven]

Roger

[north raven]

1 second

[placid sky]

Yes algebraic

[north raven]

No a polynomial can't have an irrational coefficient

Numberphile kee video par dekha tha

[placid sky]

So that’s like the complete thing, all functions involving algebraic terms, add sub multiply divide take root

[placid sky]

Idts
Like ai are all real

[north raven]

But

Aaa 🥲

[placid sky]

The coefficients can’t be imaginary

All reals work

[north raven]

In x-pi=0? pi is the coefficient of x^0

[placid sky]

Correct

[placid sky]

For ex sqrt(x)

[north raven]

Wait how would you define a transcendental number then

[placid sky]

Ahahhahahha

[north raven]

Roger

[placid sky]

There’s a very small difference

[north raven]

Between? Algebraic and transcendental numbers?

[placid sky]

No

Between right and wrong xD

[placid sky]

..

[north raven]

Achha

[placid sky]

Transcendental numbers cannot be the root of a non-zero polynomial with integer or rational coefficients.

[north raven]

Par fir transcendental numbers ko non-algebraic kyu bulate hai

[placid sky]

Well
Algebraic numbers are roots of non zero polynomials with integer/rational coefficients

Algebraic functions are a different thing

[north raven]

But algebraic equations in general can have any sort of coefficient right?

So your x-pi=0 is also an algebraic equation

Why is the naming like this for this stuff

[placid sky]

True

Wait lemme find a resource for you

You need to read

Dm me if you still have doubts

Like you have info but its in bits and pieces

[north raven]

Framing my confusion better -- how can a non-algebraic number be the solution to an algebraic equation?

[north raven]

Roger

[placid sky]

http://math.furman.edu/~dcs/courses/math10/lectures/l-6.pdf

https://www.reddit.com/r/learnmath/comments/y5p7yl/comment/iskyntt/?utm_source=share&utm_medium=mweb3x&utm_name=mweb3xcss&utm_term=1&utm_content=share_button

In short, that’s just how it’s defined lol

[placid sky]

But do read this

[north raven]

Roger

[placid sky]

This is for your last question

I’m sleepy and have classes in morning so just shared these

Drop me dms I’ll check in the morning

Good night!

[north raven]

Understandable
Thanks a lot! And roger again

[north raven]

Good nightt

[shell river]

+solved @placid sky