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

Step-by-step 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

$x {}^{3} - 3 {x}^{2} + x - 3$