Question

write a polynomial function in standard form with real coefficients whose zeros include 2, 5 i and -5 icheck the photo for more info pls!

Answer 1

Given

The zeros are given 2, 5 i and -5 i.

Step-by-step explanation

To determine the polynomial function ,

Use the general expression for the polynomial.

`(x-a)(x-b)(x-c)=0`

Substitute the values,

`(x-2)(x-5i)(x+5i)=0`

Use the identity to simplify the expression

`(a-b)(a+b)=a^2-b^2`

Then the expression becomes.

`\begin{gathered} (x-2)(x^2-(5i)^2)=(x-2)(x^2+25) \\ (x-2)(x^2+25)=x^3+25x-2x^2-50 \end{gathered}`

Answer

The answer is

`f(x)=x^3-2x^2+25x-50`