Question

Find an nth degree polynomial function with real coefficients satisfying the given conditions.

degree of the polynomial is 3; the zeros of the polynomial are 3 and i; and use f(2) = 25 to find an

Answer 1

Explanation:

Our roots are 3, and i so our roots form

will be

`(x - 3)(x - i)`

Since i is one root, it conjugate, must be the other.

so we have

`(x - 3)(x - i)(x + i)`

Simplify

`( {x}^(2) + 1)(x - 3)`

`{x}^(3) - 3 {x}^(2) + x - 3`

So the function is

`x {}^(3) - 3 {x}^(2) + x - 3`