Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

8, -14, and 3 + 9i

f(x) = x4 - 11x3 + 72x2 - 606x + 10,080
f(x) = x4 - 303x2 + 1212x - 10,080
f(x) = x4 - 11x3 - 72x2 + 606x - 10,080
f(x) = x4 - 58x2 + 1212x - 10,080

Answer 1

`f(x)=x^4-58x^2+1212x-10080`

Explanation:

The given polynomial has zeros:

`x=8,x=-14,x=3+9i`

By the complex conjugate property,
`x=3-9i` is also a zero of the polynomial.

The polynomial can be written in factored form as:

`f(x)=(x-8)(x+14)(x-(3+9i))(x-(3-9i))`

We expand to get:

`f(x)=(x^2+6x-112)(x^2-6x+90)`

We expand further to get:

`f(x)=x^4-58x^2+1212x-10080`

The last choice is correct.