Ihatenotunderstandingmath

08-08-2011, 06:56 PM

I have tried for many hours to grasp the concept of complex zeros and its use, but I have failed or it's just that my pre-calculus textbook is just written confusingly. If you don't mind, I have a few questions that I can't figure out:

1) My pre-calculus textbook tells me that the degree of a polynomial is the number of complex zeros it will have. That doesn't make sense to me because what if the equation was 3x^8 - 3? It would have -1 and 1 as it's real solutions; where does the complex number come in as a solution? (is it supposed to be 'the degree of a polynomial is the number of either real or complex zeros it will have'?)

2) What exactly IS the fundamental theorem of Algebra? My textbook says: Every complex polynomial function f(x) of degree n is greater than or equal to one has at least one complex zero.

3) What IS a complex polynomial? My textbook keeps using that but it never gives any examples of a complex polynomial. I'm assuming it's a polynomial with a complex coefficient like for example, 3i(x^2) for example?

4) I can't figure out the zeros of this problem: 2(x^4) + 5(x^3) + 5(x^2) + 20x -12 ; zero: -2i

I was thinking that since -2i is a zero and it's conjugate 2i must be a zero, we should multiply the conjugates and then divide the expression by the product. But then -2i * 2i = 4 and how are you supposed to divide the polynomial by 4? Even if you tried synethic division (assuming x - 4 as the divisor), you come up with some gigantic number. How would you solve this problem?

Thank you very much!

1) My pre-calculus textbook tells me that the degree of a polynomial is the number of complex zeros it will have. That doesn't make sense to me because what if the equation was 3x^8 - 3? It would have -1 and 1 as it's real solutions; where does the complex number come in as a solution? (is it supposed to be 'the degree of a polynomial is the number of either real or complex zeros it will have'?)

2) What exactly IS the fundamental theorem of Algebra? My textbook says: Every complex polynomial function f(x) of degree n is greater than or equal to one has at least one complex zero.

3) What IS a complex polynomial? My textbook keeps using that but it never gives any examples of a complex polynomial. I'm assuming it's a polynomial with a complex coefficient like for example, 3i(x^2) for example?

4) I can't figure out the zeros of this problem: 2(x^4) + 5(x^3) + 5(x^2) + 20x -12 ; zero: -2i

I was thinking that since -2i is a zero and it's conjugate 2i must be a zero, we should multiply the conjugates and then divide the expression by the product. But then -2i * 2i = 4 and how are you supposed to divide the polynomial by 4? Even if you tried synethic division (assuming x - 4 as the divisor), you come up with some gigantic number. How would you solve this problem?

Thank you very much!