Question

Write the simplest polynomial function with integral coefficients that had the given zeros. 7,-7i

Answer 1

To find to polynomial from zeros.

Find the factors. If it is a positive zero, the factor will be (x- zero) If it is a negative zero if is (x+zero)

Multiply the factors together.

Zeros of 7, -7i would be:

Find the factors:

`(x-7)(x\pm7i)`

Multiply the factors together: Will start out with FOIL for (x-7)(x+-7i) =

`\begin{gathered} (x-7)(x\pm7i) \\ (x-7)(x+7i)(x-7i) \\ (x-7)(x^2-7ix+7ix-49i^2) \end{gathered}`

Combine like terms. Then multiply by the last factor

`\begin{gathered} x-7(x^2-49(-1)) \\ \text{where i}^2=-1 \\ (x-7)(x^2+49) \\ x^3+49x-7x^2-343 \\ x^3-7x^2+49x-343 \end{gathered}`

Therefore the correct answer from the Option is D