Question

A polynomial function with zeros 5,5i, and -5i

Answer 1

If a, b, c are zeros of a polynomial, then the polynomial will be:
k * (x-a) * (x-b) * (x-c) where k is a constant and can be just 1.

Answer 2

So how will I write the polynomial function in standard form with those zeros 5,5i,-5i

Answer 3

First multiply (x - 5i) * (x + 5i). (use the fact that (a+b)(a-b) = a^2 - b^2)
Then multiply the above result by (x - 5).

Answer 4

So is the answer x^3-5x^2+25x-125

Answer 5

yes!

Answer 6

Any time you have roots -bi and bi you will have factor (x+bi)(x-bi) and that product always equals a sum of squares x^2 + b^2. In this case x^2 + 25. you don't have to FOIL.

Answer 7

So you only have to FOIL (x - 5)(x^2 + 25)