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

Question

n=​3;

−2

and

7+5i

are​ zeros;

Answer 1

Answer 2

So you want y = (x- [whatever one of the given zeros are] ) * ( x- [whatever one of the given zeros are] ) * (x- [whatever one of the given zeros are] ).

Since the zeros are -2 and 7+5i, you have:

y = ( x - [-2] ) * (x - [5+7i] ) * (x - [one of the given zeros])

so y = (x+2)*(x-5-7i)*((x - [one of the given zeros]) so just pick one of the zeros you already used.

so either y = (x+2)*(x-5-7i)*(x+2) OR (x+2)*(x-5-7i)*(x-5-7i)

Then make sure to simply to: either (x+2)^2 * (x-5-7i) OR y= (x+2)*(x-5-7i)^2