Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 8, -14, and 3 + 9i

Answer 1

First one 80,14 , and second one 12.

Answer 2

Explanation:

To start you need to find the factorials of 8, -14, and 3 + 9i.

The factorials of these numbers are:

8: x - 8 = 0

-14: x + 14 = 0

3 + 9i: x - 3 - 9i = 0 *

3 - 9i: x - 3 + 9i = 0 *

(If you look in the files it shows how I got these numbers)

Next, you need to multiply the factorials together.

(x - 3 - 9i)(x - 3 + 9i) = x^2 - 6x + 90

Take that and multiply by your next factorial:

(x + 14)(x^2 - 6x + 90) = x^3 + 8x^2 + 6x + 1260

Multiply that by your final factorial and you have you final answer!

(x - 8)(x^3 + 8x^2 + 6x + 1260) = x^4 + 58x^2 + 1212x - 10,080

I hoped this helped!

*When you have 3 + 9i or anything along the lines of that then you need to find the inverse of it. You simply you simply change the sign that goes before the i term. Change 3 + 9i to 3 - 9i