Question

A complex number, will, in general, have ____ fifth roots.
What is the blank?

Answer 1

hint: look at the fundamental theorem of algebra

Answer 2

Still not getting it? Can you please tell me the blank?

Answer 3

what does the fundamental theorem of algebra say?

Answer 4

"The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with zero imaginary part."

Answer 5

what else does the theorem say?

basically I'm asking this: how many roots does a 2nd degree polynomial have? what about a 3rd degree polynomial? nth degree?

Answer 6

I believe that the number of roots is equal to the number of the degree of a polynomial, right?

Answer 7

So wold the answer be 5 fifth roots?

Answer 8

you got it, the fundamental theorem of algebra also says that

if f(x) is a polynomial of degree n, then it will have n complex roots

Answer 9

*would

Answer 10

correct, the answer for the blank is 5

Answer 11

Alright! Gee, Thanks! ^.^

Answer 12

you're welcome