Who here knows the the Fundamental Theorum of Algebra is??? This was discovered by Gauss???

Question

If you know what Im talking about, then please explain what it is? thanks.

Answer 1

any nth degree polynomial equation will have n solutions and no more.
so a cubic has 3
a quadratic has 2(even if they are not real)
and so on.
now any smart people here can answer the question on my profile please?

Answer 2

Fundamental theorem of Algebra: the field C of complex numbers is algebracally closed, which means: every non-zero polynomial with coefficients in C has a root (and thus ALL of them) within the field C.
It's hard to explain fully the importance of the above theorem, but one example will probably say more than many words.
The polynomial x^2 + 1 is a polynomial with real coefficients but it has no real roots, meaning: the equation x^2 + 1 = 0 has no solutions within the field of real numbers R.
Well, this can not happen with C, according to the FTA. For example, in the case of the above equation x^2 + 1 = 0, we have two complex roots: i and -i, where i is the square root of -1, which does NOT exist in R but does exist in C.
Regards
Tonio

Answer 3

Follow this link to learn all about it:
http://en.wikipedia.org/wiki/Fundamental_Theorem_of_Algebra

It means that for every polynomial p(x) with degree n where n > 0, p(x) = 0 has exactly n solutions, counting imaginary roots and multiplicities (the same root repeated)

Example:
x^2 = 0
x * x = 0

x = 0 (or) x = 0
x = 0, 0

This is an example of multiplicities (the same root is repeated)
Here, p(x) = x^2 of degree 2. You can see that two roots are there, though repeated.

Another example:
x^3 + 2x^2 + x = 0
x(x^2 + 2x + 1) = 0

x = 0 (or) x^2 + 2x + 1 = 0
x = 0 (or) (x + 1)^2 = 0
x = 0 (or) x = -1, -1
x = 0, -1, -1

Here the roots are 0, -1, -1
Degree three
Three roots (with multiplicities)

Answer 4

The Fundamental Theorem of Algebra is a theorem about equation solving. Equivalently, the field of complex numbers is closed under algebraic operations. good luck! o and yes Gauss did discover and prove this theory.
HOOROO!

Answer 5

The number of solutions of a polynomial equation is equal to the highest power of the equation. If you have an equation ax^n + bx^(n-1) + cx^(n-2)....=0, there are n solutions. This assumes you include complex solutions, the solutions that include imaginary numbers. It also assumes that is a number is the solution more than once, you count it as more than one solution.

Answer 6

why not ask Gauss himself?

I'm sure he has a Yahoo account.

Doesn't everybody?

Answer 7

Wow haven't used this in years. I think it has something to do with roots and powers. Check wikipedia.org.

Answer 8

http://en.wikipedia.org/wiki/Divergence_theorem

Answer 9

do your own homework!