Question

Create a polynomial function that meets the following conditions:

Degree 3, 2 positive real zeros, 1 negative real zero, 0 complex zeros.
Degree 4, 2 positive real zeros, 0 negative real zeros, 2 complex zeros.

Answer 1

Try doing this - first write a polynomial of degree 3, then modify it a bit so that it has 2 positive real zeroes and so on.

Answer 2

I don't know complex numbers so I'm sorry I can't help with the second one.

Answer 3

First write a polynomial of degree three.

Answer 4

Drika, the easiest way to do it is this.
1) Decide what you want the zeros to actually be. You can pick anything as long as it first the requirements of the problem.
2) Turn those zeros into linear factors. This part is pretty simple. If the root you chose is a, then your factor will be (x-a)
3) Once you have a list of factors, multiply those together and you have your polynomial.

Answer 5

Here's a quick example:
Write a polynomial that has 1 positive real zero and 1 negative real zero

1) I need to choose the zeros I want. I'll choose:
5, -2
1 positive and 1 negative.

2) I turn my zeros into factors
5 gives me
(x-5)
-2 gives me
(x+2)

3) I have the factors (x-5) and (x+2). The last step is to multiply them together
(x-5)(x+2) =
x^2 +2x -5x -10 =
x^2 -3x -10